共查询到20条相似文献,搜索用时 31 毫秒
1.
Let L be an ample line bundle on a K3 surface. We give a sharp bound on n for which nL is k-jet ample.Received: 27 December 2002 相似文献
2.
Using the data schemes from [1] we give a rigorous definition of algebraic differential equations on the complex projective space Pn. For an algebraic subvariety S?Pn, we present an explicit formula for the degree of the divisor of solutions of a differential equation on S and give some examples of applications. We extend the technique and result to the real case. 相似文献
3.
We give a criterium on the existence of (e - 1)-very
ample linear series on a general k-gonal curve of genus $g (e \geq 1)$,
and we add some general remarks on such series. 相似文献
4.
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
5.
Bertrand To?n 《Selecta Mathematica, New Series》2005,12(1):39-134
The purpose of this work is to introduce a notion of affine stacks, which is a homotopy version of the notion of affine schemes, and to give several applications in the context of algebraic
topology and algebraic geometry.
As a first application we show how affine stacks can be used in order to give a new point of view (and new proofs) on rational
and p-adic homotopy theory. This gives a first solution to A. Grothendieck’s schematization problem described in [18].
We also use affine stacks in order to introduce a notion of schematic homotopy types. We show that schematic homotopy types give a second solution to the schematization problem, which also allows us to go beyond
rational and p-adic homotopy theory for spaces with arbitrary fundamental groups. The notion of schematic homotopy types is also used in
order to construct various homotopy types of algebraic varieties corresponding to various co-homology theories (Betti, de
Rham, l-adic, ...), extending the well known constructions of the various fundamental groups.
Finally, just as algebraic stacks are obtained by gluing affine schemes we define
$$ \infty $$-geometric stacks as a certain gluing of affine stacks. Examples of
$$ \infty $$-geometric stacks in the context of algebraic topology (moduli spaces of dga structures up to quasi-isomorphisms)
and Hodge theory (non-abelian periods) are given. 相似文献
6.
Lucia Caporaso 《manuscripta mathematica》2007,123(1):53-71
We give a combinatorial characterization of nodal curves admitting a natural (i.e. compatible with and independent of specialization)
dth Abel map for any d ≥ 1. 相似文献
7.
Andreas Gathmann 《Mathematische Annalen》2003,325(2):393-412
Let X be a smooth complex projective variety, and let be a smooth very ample hypersurface such that is nef. Using the technique of relative Gromov-Witten invariants, we give a new short and geometric proof of (a version of)
the “mirror formula”, i.e. we show that the generating function of the genus zero 1-point Gromov-Witten invariants of Y can be obtained from that of X by a certain change of variables (the so-called “mirror transformation”). Moreover, we use the same techniques to give a
similar expression for the (virtual) numbers of degree-d plane rational curves meeting a smooth cubic at one point with multiplicity 3d, which play a role in local mirror symmetry.
Received: 11 July 2001 / Published online: 4 February 2003
Funded by the DFG scholarships Ga 636/1–1 and Ga 636/1–2. 相似文献
8.
Pierre-Emmanuel Chaput 《Mathematische Zeitschrift》2002,240(2):451-459
R. Hartshorne conjectured and F. Zak proved (cf [6,p.9]) that any smooth non-degenerate complex algebraic variety with satisfies denotes the secant variety of X; when X is smooth it is simply the union of all the secant and tangent lines to X). In this article, I deal with the limiting case of this theorem, namely the Severi varieties, defined by the conditions
and . I want to give a different proof of a theorem of F. Zak classifying all Severi varieties. F. Zak proves that there exists
only four Severi varieties and then realises a posteriori that all of them are homogeneous; here I will work in another direction:
I prove a priori that any Severi variety is homogeneous and then deduce more quickly their classification, satisfying R. Lazarsfeld
et A. Van de Ven's wish [6, p.18]. By the way, I give a very brief proof of the fact that the derivatives of the equation
of Sec(X), which is a cubic hypersurface, determine a birational morphism of . I wish to thank Laurent Manivel for helping me in writing this article.
Received in final form: 29 March 2001 / Published online: 1 February 2002 相似文献
9.
Thomas Bauer 《Archiv der Mathematik》2008,90(4):317-321
In this note we give a numerical criterion that expresses the condition that an abelian variety be simple in terms of an invariant
that is closely related to the s-invariant of Ein-Cutkosky-Lazarsfeld.
Received: 1 July 2007 相似文献
10.
Hugues Verdure 《Archiv der Mathematik》2006,86(2):121-128
We give a simple criterion for the cyclicity of the m-torsion subgroup of the group of rational points on an elliptic curve defined over a finite field of characteristic larger
than 3 for m = 2, 3, 4, 6, 12.
Received: 25 January 2005 相似文献
11.
Let X be an affine surface admitting a unique affine ruling and a
-action. Assume that the ruling has a unique degenerate fibre and that this fibre is irreducible. In this paper we give a
short proof of the following result of Miyanishi and Masuda: the universal covering of X is a hypersurface in the affine 3-space given by the equation xmy = zd − 1, where m > 1.
Received: 13 June 2005 相似文献
12.
In this paper we study divisorial extremal neighborhoods such that 0 ∈ X is a cAn type threefold terminal singularity, and Γ=f(E) is a smooth curve, where E is the f-exceptional divisor. We view a divisorial extremal neighborhood as a one parameter smoothing of certain surface singularities,
and based on this we give a classification of such neighborhoods. 相似文献
13.
Sijong Kwak 《Mathematische Annalen》2001,320(4):649-664
For a projective variety X of codimension 2 in defined over the complex number field , it is traditionally said that X has no apparent -ple points if the -secant lines of X do not fill up the ambient projective space , equivalently, the locus of -ple points of a generic projection of X to ${\Bbb P}^{n+1}$ is empty. We show that a smooth threefold in has no apparent triple points if and only if it is contained in a quadric hypersurface. We also obtain an enumerative formula
counting the quadrisecant lines of X passing through a general point of and give necessary cohomological conditions for smooth threefolds in without apparent quadruple points. This work is intended to generalize the work of F. Severi [fSe] and A. Aure [Au], where
it was shown that a smooth surface in has no triple points if and only if it is either a quintic elliptic scroll or contained in a hyperquadric. Furthermore we
give open questions along these lines.
Received: 24 January 2000 / Published online: 18 June 2001 相似文献
14.
In this paper we give a geometric characterization of the cones of toric varieties that are complete intersections. In particular,
we prove that the class of complete intersection cones is the smallest class of cones which is closed under direct sum and
contains all simplex cones. Further, we show that the number of the extreme rays of such a cone, which is less than or equal
to 2n − 2, is exactly 2n − 2 if and only if the cone is a bipyramidal cone, where n > 1 is the dimension of the cone. Finally, we characterize all toric varieties whose associated cones are complete intersection
cones.
Received: 4 July 2005 相似文献
15.
H. Tutaj-Gasińska 《Monatshefte für Mathematik》2001,133(3):255-263
In this note we give a criterion for a line bundle on a general blowup of a ruled surface to be k-very ample.
(Received 29 November 2000; in revised form 2 April 2001) 相似文献
16.
Christopher D. Hacon 《Mathematische Zeitschrift》2000,235(4):717-726
The purpose of this paper is to give two applications of Fourier transforms and generic vanishing theorems:
– we give a cohomological characterization of principal polarizations
– we prove that if X an abelian variety and a polarization of type (1, ...,1,2), then a general pair is log canonical.
Received 14 May, 1999 / Published online September 14, 2000 相似文献
17.
In this short note we give a characterization of extremal principally polarized abelian varieties determining an isolated point in Sing
The case g = 5 is treated in depth.Received: 14 June 2004 相似文献
18.
《Mathematische Nachrichten》2017,290(14-15):2132-2153
19.
Sam Payne 《Mathematische Zeitschrift》2006,253(2):421-431
We show that the dual of the cone of divisors on a complete -factorial toric variety X whose stable base loci have dimension less than k is generated by curves on small modifications of X that move in families sweeping out the birational transforms of k-dimensional subvarieties of X. We give an example showing that it does not suffice to consider curves on X itself.
Supported by a Graduate Research Fellowship from the NSF 相似文献
20.
Kiwamu Watanabe 《Mathematische Annalen》2008,342(3):557-563
We give a complete classification of smooth polarized varieties (X, L) such that the linear system |L| has a homogeneous member A. 相似文献