共查询到20条相似文献,搜索用时 31 毫秒
1.
Mitsuru Kawazoe 《Journal of Pure and Applied Algebra》2006,204(3):602-615
Elliptic surfaces over an algebraically closed field in characteristic p>0 with multiple supersingular elliptic fibers, that is, multiple fibers of a supersingular elliptic curve, are investigated. In particular, it is shown that for an elliptic surface with q=g+1 and a supersingular elliptic curve as a general fiber, where q is the dimension of an Albanese variety of the surface and g is the genus of the base curve, the multiplicities of the multiple supersingular elliptic fibers are not divisible by p2. As an application of this result, the structure of false hyperelliptic surfaces is discussed on this basis. 相似文献
2.
We show the nonvanishing of H
0(X,−K
X
) for any a Fano 3-fold X for which −K
X
is a multiple of another Weil divisor in Cl(X). The main case we study is Fano 3-folds with Fano index 2: that is, 3-folds X with rank Pic(X)=1, -factorial terminal singularities and −K
X
= 2A for an ample Weil divisor A. We give a first classification of all possible Hilbert series of such polarised varieties (X,A) and deduce both the nonvanishing of H
0(X,−K
X
) and the sharp bound (−K
X
)3≥ 8/165. We find the families that can be realised in codimension up to 4. 相似文献
3.
The real partE
ℝ of a real Enriques surfaceE admits a natural decomposition in two halves,E
ℝ=E
ℝ
(1)
∪E
ℝ
(2)
, each half being a union of components ofE
ℝ. We classify the triads (E
ℝ;E
ℝ
(1)
,E
ℝ
(2)
) up to homeomorphism. Most results extend to surfaces of more general nature than Enriques surfaces. We use and study in
details the properties of Kalinin's filtration in the homology of the fixed point set of an involution, which is a convenient
tool not widely known in topology of real algebraic varieties. 相似文献
4.
Dimitra Kosta 《manuscripta mathematica》2008,127(2):151-166
We prove that for n = 8, 9, 10, 11, a nodal hypersurface of degree n in is factorial if it has at most (n − 1)2 − 1 nodes.
The author is grateful to Ivan Cheltsov for valuable comments and suggestions. 相似文献
5.
Stephan Endraß 《manuscripta mathematica》1999,99(3):341-358
For a double solid V→ℙ3> branched over a surface B⊂ℙ3(ℂ) with only ordinary nodes as singularities, we give a set of generators of the divisor class group in terms of contact surfaces of B with only superisolated singularities in the nodes of B. As an application we give a condition when H
* (˜V , ℤ) has no 2-torsion. All possible cases are listed if B is a quartic. Furthermore we give a new lower bound for the dimension of the code of B.
Received: 16 November 1998 相似文献
6.
7.
Sönke Rollenske 《manuscripta mathematica》2016,149(1-2):117-130
We construct from a general del Pezzo surface of degree 1 a Gorenstein stable surface X with \({K_X^2=1}\) and p g (X) = q(X) = 0. These surfaces are not smoothable but give an open subset of an irreducible component of the moduli space of stable Godeaux surfaces. In a particular example we also compute the canonical ring explicitly and discuss the behaviour of pluricanonical maps. 相似文献
8.
José Carlos Sierra 《Mathematische Zeitschrift》2009,262(3):517-525
Let E be a globally generated vector bundle of rank e ≥ 2 over a reduced irreducible projective variety X of dimension n defined over an algebraically closed field of characteristic zero. Let L := det(E). If deg(E) := deg(L) = L
n
> 0 and E is not isomorphic to , we obtain a sharp bound
on the degree of E, proving also that deg(L) = h
0(X, L) − n if equality holds. As an application, we obtain a Del Pezzo–Bertini type theorem on varieties of minimal degree for subvarieties
of Grassmannians, as well as a bound on the sectional genus for subvarieties of degree at most N + 1.
Research partially supported by the Spanish MCYT project MTM2006-04785 and by the program “Profesores de la UCM en el extranjero.
Convocatoria 2006”. 相似文献
9.
《Mathematische Nachrichten》2017,290(14-15):2132-2153
10.
We show that every supersingular K3 surface in characteristic 5 with Artin invariant ≤ 3 is unirational. 相似文献
11.
Yukihide Takayama 《Journal of Pure and Applied Algebra》2010,214(7):1110-1120
We consider a family of slightly extended version of Raynaud’s surfaces X over the field of positive characteristic with Mumford-Szpiro type polarizations Z, which have Kodaira non-vanishing H1(X,Z−n)≠0 for all 1≤n≤N with some N≥1. The surfaces are at least normal but smooth under a special condition. We also give a fairly large family of non-Mumford-Szpiro type polarizations Za,b with Kodaira non-vanishing. 相似文献
12.
In this paper we give a characterization of the height of K3 surfaces in characteristic p>0. This enables us to calculate the cycle classes in families of K3 surfaces of the loci where the height is at least h. The formulas for such loci can be seen as generalizations of the famous formula of Deuring for the number of supersingular
elliptic curves in characteristic p. In order to describe the tangent spaces to these loci we study the first cohomology of higher closed forms.
Received October 14, 1999 / final version received February 22, 2000?Published online May 22, 2000 相似文献
13.
C. G. Madonna 《Monatshefte für Mathematik》2005,146(4):333-339
We give infinitely many examples in which the moduli space of rank 2 H-stable sheaves on a K3 surface S endowed by a polarization H of degree 2g – 2, with Chern classes c1 = H and c2 = g – 1, is birationally equivalent to the Hilbert scheme S[g – 4] of zero dimensional subschemes of S of length g – 4. We get in this way a partial generalization of results from [5] and [1]. 相似文献
14.
Miaomiao Zhu 《Calculus of Variations and Partial Differential Equations》2009,35(2):169-189
We study Dirac-harmonic maps from degenerating spin surfaces with uniformly bounded energy and show the so-called generalized
energy identity in the case that the domain converges to a spin surface with only Neveu–Schwarz type nodes. We find condition
that is both necessary and sufficient for the W
1,2 × L
4 modulo bubbles compactness of a sequence of such maps.
Supported by IMPRS “Mathematics in the Sciences” and the Klaus Tschira Foundation. 相似文献
15.
We introduce and study a new way to categorize supersingular abelian varieties defined over a finite field by classifying them as fully maximal, mixed or fully minimal. The type of A depends on the normalized Weil numbers of A and its twists. We analyze these types for supersingular abelian varieties and curves under conditions on the automorphism group. In particular, we present a complete analysis of these properties for supersingular elliptic curves and supersingular abelian surfaces in arbitrary characteristic, and for a one-dimensional family of supersingular curves of genus 3 in characteristic 2. 相似文献
16.
Del Pezzo surfaces over with log terminal singularities of index ≤ 2 were classified by Alekseev and Nikulin. In this paper, for each of these surfaces,
we find an appropriate morphism to projective space. These morphisms enable us to describe equations of natural embeddings
of log del Pezzo surfaces of index ≤ 2 in some weighted projective space. The results obtained give a completion of similar
results of Du Val, Hidaka, and Watanabe, describing del Pezzo surfaces of index 1.
The work was done during the authors’ stay at the University of Liverpool supported by the Marie Curie program in Autumn 2004. 相似文献
17.
Jin-Xing Cai 《manuscripta mathematica》1998,95(1):273-287
LetX, Y be smooth complex projective varieties, andf: X →Y be a fiber space whose general fiber is a curve of genusg. Denote byq
f
the relative irregularity off. It is proved thatq
f
≤5g+1 / 6, iff is not generically trivial; moreover, if either a)f is non-constant and the general fiber is either hyperelliptic or bielliptic or b)q(Y)=0, thenq
f
≤g+1 / 2, and the bound is best possible.
A classification of fiber surfaces of genus 3 withq
f
=2 is also given in this note.
Project supported by China Postdoctoral Science Foundation 相似文献
18.
Nikolaus Vonessen 《manuscripta mathematica》2009,128(4):453-467
Let k be an algebraically closed base field of characteristic zero. The category equivalence between central simple algebras and
irreducible, generically free PGL
n
-varieties is extended to the context of central simple algebras with involution. The associated variety of a central simple
algebra with involution comes with an action of , where τ is the automorphism of PGL
n
given by τ (h) = (h
−1)transpose. Basic properties of an involution are described in terms of the action of on the associated variety, and in particular in terms of the stabilizer in general position for this action. 相似文献
19.
Xavier Cabré Antonio Capella Manel Sanchón 《Calculus of Variations and Partial Differential Equations》2009,34(4):475-494
We consider semi-stable, radially symmetric, and decreasing solutions of − Δ
p
u = g(u) in the unit ball of , where p > 1, Δ
p
is the p-Laplace operator, and g is a locally Lipschitz function. For this class of radial solutions, which includes local minimizers, we establish pointwise,
L
q
, and W
1,q
estimates which are optimal and do not depend on the specific nonlinearity g. Among other results, we prove that every radially decreasing and semi-stable solution u belonging to W
1,p
(B
1) is bounded whenever n < p + 4p/(p − 1). Under standard assumptions on the nonlinearity g(u) = λf (u), where λ > 0 is a parameter, it is proved that the corresponding extremal solution u
* is semi-stable, and hence, it enjoys the regularity stated in our main result. 相似文献
20.
For a simplicial subdivison Δ of a region in k
n
(k algebraically closed) and r∈N, there is a reflexive sheaf ? on P
n
, such that H
0(?(d)) is essentially the space of piecewise polynomial functions on Δ, of degree at most d, which meet with order of smoothness r along common faces. In [9], Elencwajg and Forster give bounds for the vanishing of the higher cohomology of a bundle ℰ on
P
n
in terms of the top two Chern classes and the generic splitting type of ℰ. We use a spectral sequence argument similar to
that of [16] to characterize those Δ for which ? is actually a bundle (which is always the case for n= 2). In this situation we can obtain a formula for H
0(?(d)) which involves only local data; the results of [9] cited earlier allow us to give a bound on the d where the formula applies. We also show that a major open problem in approximation theory may be formulated in terms of a
cohomology vanishing on P
2 and we discuss a possible connection between semi-stability and the conjectured answer to this open problem.
Received: 9 April 2001 相似文献