共查询到20条相似文献,搜索用时 31 毫秒
1.
Let D be an integral domain with quotient field K, X be an indeterminate over D, Γ be a numerical semigroup with Γ ? ?0, D[Γ] be the semigroup ring of Γ over D (and hence D ? D[Γ] ? D[X]), and D + X n K[X] = {a + X n g∣a ∈ D and g ∈ K[X]}. We show that there exists an order-preserving bijection between Spec(D[X]) and Spec(D[Γ]), which also preserves t-ideals. We also prove that D[Γ] is an APvMD (resp., AGCD-domain) if and only if D[X] is an APvMD (resp., AGCD-domain) and char(D) ≠ 0. We show that if n ≥ 2, then D is an APvMD (resp., AGCD-domain, AGGCD-domain, AP-domain, AB-domain) and char(D) ≠ 0 if and only if D + X n K[X] is an APvMD (resp., AGCD-domain, AGGCD-domain, AP-domain, AB-domain). Finally, we give some examples of APvMDs which are not AGCD-domains by using the constructions D[Γ] and D + X n K[X]. 相似文献
2.
In this article, we construct examples of n-folds X carrying an ample line bundle A ∈ Pic X such that property N p fails for K X + (n + 1 + p)A. This shows that the condition of Mukai's conjecture is optimal for every n ≥ 1 and p ≥ 0. 相似文献
3.
Cédric Pépin 《Mathematische Annalen》2013,355(1):147-185
Let S be the spectrum of a discrete valuation ring with function field K. Let X be a scheme over S. We will say that X is semi-factorial over S if any invertible sheaf on the generic fiber X K can be extended to an invertible sheaf on X. Here we show that any proper geometrically normal scheme over K admits a proper, flat, normal and semi-factorial model over S. We also construct some semi-factorial compactifications of regular S-schemes, such as Néron models of abelian varieties. The semi-factoriality property for a scheme X/S corresponds to the Néron property of its Picard functor. In particular, one can recover the Néron model of the Picard variety ${{\rm Pic}_{X_K/K,{\rm red}}^0}$ of X K from the Picard functor Pic X/S , as in the known case of curves. This provides some information on the relative algebraic equivalence on the S-scheme X. 相似文献
4.
5.
Gyu Whan Chang 《代数通讯》2013,41(10):4182-4187
Let α be an infinite cardinal number, Λ be an index set of cardinality > α, and {X λ}λ∈Λ be a set of indeterminates over an integral domain D. It is well known that there are three ways of defining the ring of formal power series in {X λ}λ∈Λ over D, say, D[[{X λ}]] i for i = 1, 2, 3. In this paper, we let D[[{X λ}]]α = ∪ {D[[{X λ}λ∈Γ]]3 | Γ ? Λ and |Γ| ≤ α}, and we then show that D[[{X λ}]]α is an integral domain such that D[[{X λ}]]2 ? D[[{X λ}]]α ? D[[{X λ}]]3. We also prove that (1) D is a Krull domain if and only if D[[{X λ}]]α is a Krull domain and (2) D[[{X λ}]]α is a unique factorization domain (UFD) (resp., π-domain) if and only if D[[X 1,…, X n ]] is a UFD (resp., π-domain) for every integer n ≥ 1. 相似文献
6.
Simone Diverio 《Mathematische Annalen》2009,344(2):293-315
Let be a smooth complex projective hypersurface. In this paper we show that, if the degree of X is large enough, then there exist global sections of the bundle of invariant jet differentials of order n on X, vanishing on an ample divisor. We also prove a logarithmic version, effective in low dimension, for the log-pair , where D is a smooth irreducible divisor of high degree. Moreover, these result are sharp, i.e. one cannot have such jet differentials
of order less than n. 相似文献
7.
I. Alrasasi 《代数通讯》2013,41(4):1385-1400
Let D be an integral domain with quotient field K. A Bhargava ring over D is defined to be 𝔹 x (D): = {f ∈ K[X] | ? a ∈ D, f(xX + a) ∈ D[X]}, where x ∈ D. A Bhargava ring over D is a subring of the ring of integer-valued polynomials over D. In this article, we study the prime ideal structure and calculate the Krull and valuative dimension of Bhargava rings over a general domain D. 相似文献
8.
9.
Nicholas J. Werner 《代数通讯》2013,41(12):4717-4726
When D is a commutative integral domain with field of fractions K, the ring Int(D) = {f ∈ K[x] | f(D) ? D} of integer-valued polynomials over D is well-understood. This article considers the construction of integer-valued polynomials over matrix rings with entries in an integral domain. Given an integral domain D with field of fractions K, we define Int(M n (D)): = {f ∈ M n (K)[x] | f(M n (D)) ? M n (D)}. We prove that Int(M n (D)) is a ring and investigate its structure and ideals. We also derive a generating set for Int(M n (?)) and prove that Int(M n (?)) is non-Noetherian. 相似文献
10.
Burkhard Külshammer 《代数通讯》2013,41(1):147-168
Abstract Let D be an integral domain. A multiplicative set S of D is an almost splitting set if for each 0 ≠ d ∈ D, there exists an n = n(d) with d n = st where s ∈ S and t is v-coprime to each element of S. An integral domain D is an almost GCD (AGCD) domain if for every x, y ∈ D, there exists a positive integer n = n(x, y) such that x n D ∩ y n D is a principal ideal. We prove that the polynomial ring D[X] is an AGCD domain if and only if D is an AGCD domain and D[X] ? D′[X] is a root extension, where D′ is the integral closure of D. We also show that D + XD S [X] is an AGCD domain if and only if D and D S [X] are AGCD domains and S is an almost splitting set. 相似文献
11.
Adeleh Abdolghafourian 《代数通讯》2013,41(7):2852-2862
Let X be a nonempty set of positive integers and X* = X?{1}. The divisibility graph D(X) has X* as the vertex set, and there is an edge connecting a and b with a, b ∈ X* whenever a divides b or b divides a. Let X = cs(G) be the set of conjugacy class sizes of a group G. In this case, we denote D(cs(G)) by D(G). In this paper, we will find the number of connected components of D(G) where G is the symmetric group S n or is the alternating group A n . 相似文献
12.
Karen E. Smith 《代数通讯》2013,41(12):5915-5929
Abstract For a canonical threefold X, we know that h 0(X, 𝒪 X (nK X )) ≥ 1 for a sufficiently large n. When χ(𝒪 X ) > 0, it is not easy to get such an integer n. Fletcher showed that h 0(X, 𝒪 X (12K X )) ≥ 1 and h 0(X, 𝒪 X (24K X )) ≥ 2 when χ(𝒪 X ) = 1. He inquired about existence of a canonical threefold with given conditions which shows the result sharp. We show that such an example does not exist. Using a different technique, we prove h 0(X, 𝒪 X (12K X )) ≥ 2. 相似文献
13.
Sönke Rollenske 《Mathematische Annalen》2008,341(3):623-628
The Frölicher spectral sequence of a compact complex manifold X measures the difference between Dolbeault cohomology and de Rham cohomology. If X is Kähler then the spectral sequence collapses at the E 1term and no example with d n ≠ 0 for n > 3 has been described in the literature.We construct for n ≥ 2 nilmanifolds with left-invariant complex structure X n such that the n-th differential d n does not vanish. This answers a question mentioned in the book of Griffiths and Harris. 相似文献
14.
Lukas Katthän 《代数通讯》2013,41(8):3290-3300
Let R = K[X1, ?c, Xn] be a polynomial ring over some field K. In this article, we prove that the kth syzygy module of the residue class field K of R has Stanley depth n ? 1 for ?n/2? ≤k < n, as it had been conjectured by Bruns et al. in 2010. In particular, this gives the Stanley depth for a whole family of modules whose graded components have dimension greater than 1. So far, the Stanley depth is known only for a few examples of this type. Our proof consists in a close analysis of a matching in the Boolean algebra. 相似文献
15.
Gianluca Occhetta 《manuscripta mathematica》2001,104(1):111-121
In this paper we classify pairs (X,ℰ) with ℰ ample vector bundle of rank r on a smooth variety X of dimension n= 2r−1 such that K
X
+ det ℰ=?
x
.
Received: 7 April 2000 相似文献
16.
Davide Fusi 《代数通讯》2013,41(8):2989-3008
Let X be a smooth complex projective variety and let Z ? X be a smooth submanifold of dimension ≥ 2, which is the zero locus of a section of an ample vector bundle ? of rank dim X ? dim Z ≥ 2 on X. Let H be an ample line bundle on X, whose restriction H Z to Z is generated by global sections. The structure of triplets (X,?,H) as above is described under the assumption that the curve genus of the corank-1 vector bundle ? ⊕ H ⊕ (dim Z?1) is ≤ h 1( X ) + 2. 相似文献
17.
We prove that any sequence of 4-dimensional log flips that begins with a klt pair (X,D) such that -(K
X
+D) is numerically equivalent to an effective divisor, terminates. This implies termination of flips that begin with a log Fano
pair and termination of flips in a relative birational setting. We also prove termination of directed flips with big K
X
+D. As a consequence, we prove existence of minimal models of 4-dimensional dlt pairs of general type, existence of 5-dimensional
log flips, and rationality of Kodaira energy in dimension 4. 相似文献
18.
Edoardo Ballico 《代数通讯》2013,41(11):4257-4262
Let X ? ? n be a complex nondegenerate projective variety of dimension m ≥ 2. For t ≤ n ? m and a general q ∈ ? n , the linear space L q spanned by q and t general points of X meets X in a finite set of points. We classify those X ? ? n for which there exists a point q ∈ ? n such that L q meets X in a positive dimensional variety. If this occurs, there exists d ≤ n ? m such that a degree d rational normal curve through d general points of X is contained in X. Examples of this situation are provided. An infinitesimal generalization of part of the main result is also stated. 相似文献
19.
Priska Jahnke Thomas Peternell Ivo Radloff 《Central European Journal of Mathematics》2011,9(3):449-488
In a follow-up to our paper [Threefolds with big and nef anticanonical bundles I, Math. Ann., 2005, 333(3), 569–631], we classify
smooth complex projective threefolds Xwith −K
X
big and nef but not ample, Picard number γ(X) = 2, and whose anticanonical map is small. We assume also that the Mori contraction of X and of its flop X
+ are not both birational. 相似文献
20.
Gyu Whan Chang 《代数通讯》2013,41(7):2650-2664
Let D be an integral domain, S be a (saturated) multiplicative subset of D such that D ? D S , Γ be a numerical semigroup with Γ ? ?0, Γ* = Γ?{0}, X be an indeterminate over D, D + XD S [X] = {a + Xg ∈ D S [X]∣a ∈ D and g ∈ D S [X]}, and D + D S [Γ*] = {a + f ∈ D S [Γ]∣a ∈ D and f ∈ D S [Γ*]}; so D + D S [Γ*] ? D + XD S [X]. In this article, we study when D + D S [Γ*] is an APvMD, an AGCD-domain, an AS-domain, an AP-domain, or an AB-domain. 相似文献