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1.
Yunhe Sheng 《代数通讯》2013,41(5):1929-1953
Let Y be an integral projective curve whose singularities are of type Ak, i.e. with only tacnodes and planar (perhaps non-ordinary) cusps. Set g:= pa(Y). Here we study the Brill - Noether theory of spanned line bundles on Y. If the singularities are bad enough, we show the existence of spanned degree d line bundles, L, with h0(Y, L) ≥ r + 1 even if the Brill - Noether number ρ(g, d, r) < 0. We apply this result to prove that genus g curves with certain singularities cannot be hyperplane section of a simple K3 surface S ? P g. 相似文献
2.
Yoshiaki Fukuma 《Mathematische Nachrichten》1996,180(1):75-84
Let X be a smooth projective variety over ? and L be a nef-big divisor on X. Then (X, L) is called a quasi - polarized manifold. Then we conjecture that g(L) ≥ q(X), where g(L) is the sectional genus of L and q(X) = dim H1(Ox) is the irregularity of X. In general it is unknown that this conjecture is true or not even in the case of dim X = 2. For example, this conjecture is true if dim X = 2 and dim H≥(L) > 0. But it is unknown if dim X ≥ 3 and dim H0(L) > 0. In this paper, we consider a lower bound for g(L) if dim X = 2, dim H0(L) ≥ 2, and k(X) ≥ 0. We obtain a stronger result than the above conjecture if dim Bs|L| ≤ 0 by a new method which can be applied to higher dimensional cases. Next we apply this method to the case in which dim X = n ≥ 3 and we obtain a lower bound for g(L) if dim X = 3, dim H0(L) ≥ 2, and k(X) ≥ 0. 相似文献
3.
Here we prove the following result.
Theorem 1.1.Let X be an integral projective curve of arithmetic genus g and k≧ ≧4 an integer. Assume the existence of L ∈ Pick
(X) with h
0
(X, L)=2 and L spanned. Fix a rank 1 torsion free sheaf M on X with h
0(X,M)=r+1≧2, h1
(X, M)≧2 and M spanned by its global sections. Set d≔deg(M) and s≔max {n≧0:h
0 (X, M ⊗(L*)⊗n)>0}. Then one of the following cases occur:
We find also other upper bounds onh
0 (X, F).
(a) | M≊L ⊗r; |
(b) | M is the subsheaf of ω X⊗(L*)⊗t, t:=g−d+r−1, spanned by H0(X, ωX⊗(L*)⊗t); |
(c) | there is a rank 1 torsion free sheaf F on X with 1≦h 0(X, F)≦k−2 such that M≊L⊗s⊗F. Moreover, if we fix an integer m with 2≦m≦k−2 and assume r#(s+1)k−(ns+n+1) per every 2≦n≦m, we have h0 (X, F)≦k−m−1. |
Sunto In questo lavoro si dimostra il seguente teorema. Teorem 1.1.Sia X una curva proiettiva ridotta e irriducibile di genere aritmetico g e k≥4 un intero. Si supponga l'esistenza di L ε Pick (X) con h 0 (X, L)=2 e L generato. Si fissi un fascio senza torsione di rango uno M su X con h0 (X, M)=r++1≥2, h1 (X, M) ≧2 e M generato dalle sue sezioni globali. Si ponga d≔deg(M) e s≔max{n≧0:h 0(X, M ⊗(L*)⊗n)>0}. Allora si verifica uno dei casi seguenti:相似文献Si ricavano anche altre maggiorazioni suh 0,(X, F).
(a) M≊L ⊗r; (b) M è il sottofascio di ω X⊗(L*)⊗t, t:=g−d+r−1 generato da H0 (X, ωX⊗(L*)⊗t); (c) esiste un fascio senza torsione di rango un F su X con 1≦h 0 (X, F) <=k−2 tale che M ≊L ⊗8 ⊗ F. Inoltre, se si fissa un intero m con 2≦m≦k−2 e si suppone r#(s+1) k−(ns+n+1) per ogni 2≦n≦m, si ottiene h 0 (X, F)≦k−m−1.
4.
Yoshiaki Fukuma 《Arkiv f?r Matematik》1997,35(2):299-311
Let (X, L) be a polarized 3-fold over the complex number field. In [Fk3], we proved thatg(L)≥q(X) ifh
0(L)≥2 and moreover we classified (X, L) withh
0(L)≥3 andg(L)=q(X), whereg(L) is the sectional genus of (X, L) andq(X)=dimH
1(O
X
) the irregularity ofX. In this paper we will classify polarized 3-folds (X, L) withh
0(L)≥4 andg(L)=q(X)+1 by the method of [Fk3]. 相似文献
5.
Let X be a reduced and irreducible projective variety of dimension d. Let π:X→Y be a separable noetherian normalization of X and ? the canonical morphism Ωd X/k→Ωd L/k. From our main result: $$J_X \varphi (\pi ^* \Omega ^d _{Y/k} ) = \theta _k (X/Y)\varphi (\Omega ^d _{X/k} )$$ we deduce relations among: complementary module C(X/Y), Kähler different θk(X/Y), Dedekind different θD(X/Y), jacobian ideal JK and ω-jacobian ideal \(\tilde J_X\) . 相似文献
6.
《Quaestiones Mathematicae》2013,36(3-4):321-334
Abstract The group ?(Mm(A) v Mn(π)) of homotopy self-equivalence classes of two Moore spaces is faithfully represented onto a (multiplicative) group of matrices for n≥m≥3. We consider, in this note, related representations of ?(Mm(Λ)vMn(π)), for finitely generated Λ and π in the case where n≥4, and also where n=3 if ext(Λ, π)=0. The representation onto a matrix group, similar to that in the case above, is not, in general, valid. We show however that ?(M2(Λ)vMn(π)) is represented onto ?(M2(Λ))× ?(Mn(π) in this case, and that this representation determines an isomorphism with an iterated semi-direct product ?(M2(Λ)v Mn(π)) ? {(Mn(π), M2(Λ))? ext(π Λ ? π)} ? (?(M2(Λ)) × ? (Mn(π)). More generally we review, and-extend, the theory of the representation of the (generalized) near ring (XvY,XvY) onto the matrix (generalized) near-ring (XvY, XxY) where appropriate, in the case where X and Y are h-coloops; and we deduce results for the representation of ?(XvY, XvY). Some of the results published previously in the case of simply-connected CW co-h-spaces, extend to the case where X and Y are path-connected h-coloops one of which is well-pointed. We note the obstructions to the existence of a homomorphic section, and consider a number of special cases which occur when some of the groups are trivial. 相似文献
7.
Given a cotriple 𝔾 = (G, ε, δ) on a category X and a functor E:X Opp→A into an abelian category A, there exists the cohomology theory of Barr and Beck: Hn(X, E) ε |A| (n ≥ 0, X ε |X|), ([1], p.249). Almost all the important cohomology theories in mathematics have been shown to be special instances of such a general theory (see [1], [2] and [3]). Usually E arises from an abelian group object Y in X in the following manner: it is the contravariant functor from X into the category Ab of abelian groups that associates to each object X in X the abelian group X(X, Y) of maps from X to Y. In such a situation we shall write Hn(X, Y)𝔾 instead of Hn(X, E)G. Barr and Beck [2] have shown that the Eilenberg-MacLane cohomology groups H?n(π, A), n ≥ 2, can be re-captured as follows. One considers the free group cotriple 𝔾′ on the category Gps of groups, which induces in a natural manner a cotriple 𝔾 on the category (Gps, π) of groups over a fixed group π. 相似文献
8.
Litan Yan 《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(1-2):47-56
Let X =( X t ) t S 0 be a continuous semimartingale given by d X t = f ( t ) w ( X t )d d M ¢ t + f ( t ) σ ( X t )d M t , X 0 =0, where M =( M t , F t ) t S 0 is a continuous local martingale starting at zero with quadratic variation d M ¢ and f ( t ) is a positive, bounded continuous function on [0, X ), and w , σ both are continuous on R and σ ( x )>0 if x p 0. Denote X 𝜏 * =sup 0 h t h 𝜏 | X t | and J t = Z 0 t f ( s ) } ( X s )d d M ¢ s ( t S 0) for a nonnegative continuous function } . If w ( x ) h 0 ( x S 0) and K 1 | x | n σ 2 ( x ) h | w ( x )| h K 2 | x | n σ 2 ( x ) ( x ] R , n >0) with two fixed constants K 2 S K 1 >0, then under suitable conditions for } we show that the maximal inequalities c p , n log 1 n +1 (1+ J 𝜏 ) p h Á X 𝜏 * Á p h C p , n log 1 n +1 (1+ J 𝜏 ) p (0< p < n +1) hold for all stopping times 𝜏 . 相似文献
9.
Yoshiaki Fukuma 《Geometriae Dedicata》1998,69(2):189-206
Let (X,L) be a polarized surface. If h0(L)>0, then g(L) q(X). In our previous papers, we classified polarized surfaces (X,L) with g(L)=q(X) and h0(L)>0. In this paper, we classify polarized surfaces (X,L) with g(L)=q(X)+1, h0(L)>0, and (X) 0. 相似文献
10.
Bokhee Im 《Results in Mathematics》1994,25(1-2):60-63
Let K be a commutative ordered field and L =K(i) the quadratic extension of K with i2 = ?1. Let H be the set of all Hermitian 2 × 2 matrices over the field extension (L,K) and let H(2),+ ? {A ∈ H ¦ det A ∈ K(2), Tr A > 0}. Then we prove that (H(2),+,⊕) is a K-loop with respect to the operation $$ {\rm A}\ \oplus \ {\rm B}= {1 \over {\rm TrA} + 2{\sqrt {\rm det A}}} ({\sqrt {\rm det A}}\ E +A){\rm B} ({\sqrt {\rm det A}}\ E +A) $$ where E is the identity matrix. 相似文献
11.
Marek Fila Howard A. Levine Yoshitaka Uda 《Mathematical Methods in the Applied Sciences》1994,17(10):807-835
In this paper we condiser non-negative solutions of the initial value problem in ?N for the system where 0 ? δ ? 1 and pq > 0. We prove the following conditions. Suppose min(p,q)≥1 but pq1.
- (a) If δ = 0 then u=v=0 is the only non-negative global solution of the system.
- (b) If δ>0, non-negative non-globle solutions always exist for suitable initial values.
- (c) If 0<?1 and max(α, β) ≥ N/2, where qα = β + 1, pβ = α + 1, then the conclusion of (a) holds.
- (d) If N > 2, 0 < δ ? 1 and max (α β) < (N - 2)/2, then global, non-trivial non-negative solutions exist which belong to L∞(?N×[0, ∞]) and satisfy 0 < u(X, t) ? c∣x∣?2α and 0 < v(X, t) ? c ∣x∣?2bT for large ∣x∣ for all t > 0, where c depends only upon the initial data.
- (e) Suppose 0 > δ 1 and max (α, β) < N/2. If N> = 1,2 or N > 2 and max (p, q)? N/(N-2), then global, non-trivial solutions exist which, after makinng the standard ‘hot spot’ change of variables, belong to the weighted Hilbert space H1 (K) where K(x) ? exp(¼∣x∣2). They decay like e[max(α,β)-(N/2)+ε]t for every ε > 0. These solutions are classical solutions for t > 0.
- (f) If max (α, β) < N/2, then threre are global non-tivial solutions which satisfy, in the hot spot variables where where 0 < ε = ε(u0, v0) < (N/2)?;max(α, β). Suppose min(p, q) ? 1.
- (g) If pq ≥ 1, all non-negative solutions are global. Suppose min(p, q) < 1.
- (h) If pg > 1 and δ = 0, than all non-trivial non-negative maximal solutions are non-global.
- (i) If 0 < δ ? 1, pq > 1 and max(α,β)≥ N/2 all non-trivial non-negative maximal solutions are non-global.
- (j) If 0 < δ ≥ 1, pq > 1 and max(α,β) < N/2, there are both global and non-negative solutions.
12.
Christopher J. Winfield 《Journal of Geometric Analysis》2001,11(2):343-362
In this article the following class of partial differential operators is examined for local solvability: Let P(X, Y) be a homogeneous polynomial of degree n ≥ 2 in the non-commuting variables X and Y. Suppose that the complex polynomial P(iz, 1) has distinct roots and that P(z, 0) = zn. The operators which we investigate are of the form P(X, Y) where X = δx and Y = δy + xδw for variables (x, y, w) ∈ ?3. We find that the operators P (X, Y) are locally solvable if and only if the kernels of the ordinary differential operators P(iδx, ± x)* contain no Schwartz-class functions other than the zero function. The proof of this theorem involves the construction of a parametrix along with invariance properties of Heisenberg group operators and the application of Sobolev-space inequalities by Hörmander as necessary conditions for local solvability. 相似文献
13.
Real hypersurfaces of a complex manifold admit a naturally induced almost contact structure F′ from the almost complex structure of the ambient manifold. We prove that for any F′-invariant submanifold M of a geodesic hypersphere in a non-flat complex space form and of a horosphere in a complex hyperbolic space, its second
fundamental form h satisfies the condition h(FX,Y ) - h(X, FY) = g(FX, Y )h, X,Y ? T(M), 0 1 h ? T^(M){h(FX,Y ) - h(X, FY) = g(FX, Y )\eta, X,Y \in T(M), 0 \ne \eta \in {T^\perp}(M)}, which has been considered in [2] and [3]. 相似文献
14.
Edward A. Bender E. Rodney Canfield Brendan D. McKay 《Random Structures and Algorithms》1990,1(2):127-169
Let c(n, q) be the number of connected labeled graphs with n vertices and q ≤ N = (2n ) edges. Let x = q/n and k = q ? n. We determine functions wk ? 1. a(x) and φ(x) such that c(n, q) ? wk(qN)enφ(x)+a(x) uniformly for all n and q ≥ n. If ? > 0 is fixed, n→ ∞ and 4q > (1 + ?)n log n, this formula simplifies to c(n, q) ? (Nq) exp(–ne?2q/n). on the other hand, if k = o(n1/2), this formula simplifies to c(n, n + k) ? 1/2 wk (3/π)1/2 (e/12k)k/2nn?(3k?1)/2. 相似文献
15.
E. I. Pancheva 《Journal of Mathematical Sciences》2000,99(3):1306-1316
Let g be the distribution function (d.f.) of an extremal process Y. If g is invariant with respect to a continuous one-parameter
group of time-space changes {ηα = (τα, Lα): α > 0}, i.e. g ∘ ηα = g ∀ α > 0, then g is self-similar. If g is invariant w.r.t. the cyclic group {η∘(n), n ∈Z} of a time-space change ν, then g is semi-self-similar. The semi-self-similar extremal processes are limiting for sequences
of extremal processes Yn(t)=L
n
−1
∘ Y ∘ τn (t) if going along a geometrically increasing subsequence kn ∼ ϕn, ϕ > 1, n → ∞. The main properties of multivariate semi-self-similar extremal processes and some examples are discussed in
the paper. The results presented are an analog of the theory of semi-self-similar processes with additive increments developed
by Maejima and Sato in 1997.
Supported by the Bulgarian Ministry of Education and Science (grant No. MM-705/97).
Proceedings of the Seminar on Stability Problems for Stochastic Models, Vologda, Russia, 1998, Part I. 相似文献
16.
B. P. Osilenker 《Mathematical Notes》2007,82(3-4):366-379
We study discrete Sobolev spaces with symmetric inner product $$\left\langle {f,g} \right\rangle _\alpha = \int_{ - 1}^1 {f g d\mu _\alpha } + M[f(1)g(1) + f( - 1)g( - 1)] + K[f'(1)g'(1) + f'( - 1)g'( - 1)]$$ , where M ≥ 0, k ≥ 0, and $$d\mu _\alpha (x) = \frac{{\Gamma (2\alpha + 2)}}{{2^{2\alpha + 1} \Gamma ^2 (\alpha + 1)}}(1 - x^2 )^\alpha dx, \alpha > - 1$$ , is the Gegenbauer probability measure. We obtain the solution of the following extremal problem: Calculate $$\mathop {\inf }\limits_{a_0 ,a_1 ,...,a_{N - r} } \left\{ {\langle P_N^{(r)} ,P_N^{(r)} \rangle _\alpha ,1 \leqslant r \leqslant N - 1, P_N^{(r)} (x) = \sum\limits_{j = N - r + 1}^N {a_j^0 x^j } + \sum\limits_{j = 0}^{N - r} {a_j x^j } } \right\}$$ , where the a j 0 , j = N ? r + 1, N ? r + 2, ..., N ? 1, N, a N 0 > 0, are fixed numbers, and find the extremal polynomial. 相似文献
17.
<正> 引言 关于复合形或更一般的空間在欧氏空間中的实現問題,Whitney和Thom分別有下面的結果: 定理.(Whitney)n維紧致微分流形M~n可微分实現于R~N中的必要条件为 W~k(M~n)=0,k≥N-n.(1) 定理.(Thom)一个有可数基而局部可縮的紧致Hausdorff空間X可以拓扑实現 相似文献
18.
Frank Gerth 《Journal of Number Theory》1983,17(2):191-203
Let K be a cyclic Galois extension of the rational numbers Q of degree ?, where ? is a prime number. Let h? denote the order of the Sylow ?-subgroup of the ideal class group of K. If h? = ?s(s ≥ 0), it is known that the number of (finite) primes that ramify in K/Q is at most s + 1 (or s + 2 if K is real quadratic). This paper shows that “most” of these fields K with h? = ?s have exactly s + 1 ramified primes (or s + 2 ramified primes if K is real quadratic). Furthermore the Sylow ?-subgroup of the ideal class group is elementary abelian when h? = ?s and there are s + 1 ramified primes (or s + 2 ramified primes if K is real quadratic). 相似文献
19.
It is well known how the Kostant-Rowen Theorem extends the validity of the famous Amitsur-Levitzki identity to skew-symmetric matrices. Here we give a general method, based on a graph theoretic approach, for deriving extensions of known permanental-type identities to skew-symmetric and symmetric matrices over a commutative ring of prime characteristic. Our main result has a typical Kostant-Rowen flavour: IfM≥p[n+1/2] then $C_M (X,Y) = \sum\limits_{\alpha ,\beta \in Sym(M)} {x_{\alpha (1)} y_{\beta (1)} x_{\alpha (2)} y_{\beta (2)} } ...x_{\alpha (M)} y_{\beta (M)} = 0$ is an identity onM n ? (Ω), the set ofnxn skew-symmetric matrices over a commutative ring Ω withp1Ω=0 (provided that $P > \sqrt {[n + 1/2)} $ ). Otherwise, the stronger conditionM≥pn implies thatC M(X,Y)=0 is an identity on the full matrix ringM n(Ω). 相似文献
20.
Let L be any of simple Lie algebras of Cartan type L = X(2)(m : n : Φ), X = 5, H or K, n≠1, over a field F of characteristic p > 3, and R a commutative ring extension of F. Then AutR(R?L)≌ Aut R(R?21 (m : n) : R?L). It follows that, all forms of L are standard and thereby are determined 相似文献