共查询到20条相似文献,搜索用时 15 毫秒
1.
David Cox 《Journal of Pure and Applied Algebra》2007,209(3):651-669
Let XP be a smooth projective toric variety of dimension n embedded in Pr using all of the lattice points of the polytope P. We compute the dimension and degree of the secant variety . We also give explicit formulas in dimensions 2 and 3 and obtain partial results for the projective varieties XA embedded using a set of lattice points A⊂P∩Zn containing the vertices of P and their nearest neighbors. 相似文献
2.
3.
The Severi variety parameterizes plane curves of degree d with δ nodes. Its degree is called the Severi degree. For large enough d, the Severi degrees coincide with the Gromov–Witten invariants of CP2. Fomin and Mikhalkin (2010) [10] proved the 1995 conjecture that for fixed δ, Severi degrees are eventually polynomial in d. 相似文献
4.
We show that any smooth Q-normal lattice polytope P of dimension n and degree d is a strict Cayley polytope if n?2d+1. This gives a sharp answer, for this class of polytopes, to a question raised by V.V. Batyrev and B. Nill. 相似文献
5.
Joaquín Moraga 《Journal of Pure and Applied Algebra》2019,223(8):3225-3237
In this note, we study linear systems on complete toric varieties X with an invariant point whose orbit under the action of contains the dense torus T of X. We give a characterization of such varieties in terms of its defining fan and introduce a new definition of expected dimension of linear systems which consider the contribution given by certain toric subvarieties. Finally, we study degenerations of linear systems on these toric varieties induced by toric degenerations. 相似文献
6.
For affine toric varieties X and defined by dual cones, we define an equivalence of categories between mixed versions of the equivariant derived category and the derived category of sheaves on which are locally constant with unipotent monodromy on each orbit. This equivalence satisfies the Koszul duality formalism of Beilinson, Ginzburg, and Soergel. 相似文献
7.
Sukmoon Huh 《Journal of Pure and Applied Algebra》2011,215(9):2099-2105
We prove that the moduli space of stable sheaves of rank 2 with the Chern classes c1=OQ(1,1) and c2=2 on a smooth quadric Q in P3 is isomorphic to P3. Using this identification, we give a new proof that a Brill-Noether locus, defined as the closure of the stable bundles with at least three linearly independent sections, on a non-hyperelliptic curve of genus 4, is isomorphic to the Donagi-Izadi cubic threefold. 相似文献
8.
Sandra Di Rocco 《Mathematische Zeitschrift》1999,231(1):169-188
The notion of a k-convex -support function for a toric variety is introduced. A criterion for a line bundle L to generate k-jets on X is given in terms of the k-convexity of the -support function . Equivalently L is proved to be k-jet ample if and only if the restriction to each invariant curve has degree at least k.
Received October 22, 1997; in final form January 12, 1998 相似文献
9.
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
11.
Let p:
E B
be a principal bundle with fibre and structure
group the torus T (
*)n over a
topological space B.
Let X be a nonsingular projective
T-toric variety.
One has the X-bundle
: E(X)
B where
E(X)
= E ×
T
X,
([e,x])
= p(e).
This is a Zariski locally trivial fibre bundle
in case p:
E
B is algebraic. The purpose of this
note is to describe (i) the singular cohomology ring of
E(X)
as an H
*
(B;)-algebra,
(ii) the topological K-ring of
K
*
(E(X))
as a K
*
(B)-algebra when
B is compact.
When p :
E
B is algebraic over an irreducible,
nonsingular, noetherian scheme over
, we describe (iii) the Chow ring of
A
*
(E(X))
as an A
*
(B)-algebra, and
(iv) the Grothendieck ring $\mathcal K$0
(E
(X)) of algebraic vector
bundles on E
(X) as a
$\mathcal K$0(B)-algebra. 相似文献
12.
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
13.
This article is a survey of basic facts about the moduli spaces of stable surfaces. These spaces are projective compactifications of the moduli spaces of minimal surfaces of general type. They share few of the nice features of the moduli spaces of stable curves. Some of the main pathologies are presented with some historical remarks and some more recent results on the boundary of these spaces.Received: February, 2004 相似文献
14.
Mihai Halic 《Mathematische Zeitschrift》2006,252(1):157-208
We present a purely algebraic approach to the Hamiltonian / Gauge theoretical invariants associated to torus actions on affine
spaces. Secondly, we address the issue of computing the invariants: a localization and a genus recursion formula are deduced.
Partially supported by: EAGER - European Algebraic Geometry Research Training Network, contract No. HPRN-CT-2000-00099 (BBW). 相似文献
15.
Kōta Yoshioka 《Mathematische Annalen》2001,321(4):817-884
In this paper, we consider basic problems on moduli spaces of stable sheaves on abelian surfaces. Our main assumption is
the primitivity of the associated Mukai vector. We determine the deformation types, albanese maps, Bogomolov factors and their
weight 2 Hodge structures. We also discuss the deformation types of moduli spaces of stable sheaves on K3 surfaces.
Received: 28 February 2000 / Revised version: 15 September 2000 / Published online: 24 September 2001 相似文献
16.
Bernt Ivar Utstøl Nødland 《Journal of Pure and Applied Algebra》2018,222(3):508-533
We use Matsui and Takeuchi's formula for toric A-discriminants to give algorithms for computing local Euler obstructions and dual degrees of toric surfaces and 3-folds. In particular, we consider weighted projective spaces. As an application we give counterexamples to a conjecture by Matsui and Takeuchi. As another application we recover the well-known fact that the only defective normal toric surfaces are cones. 相似文献
17.
We classify moduli spaces of arrangements of 10 lines with quadruple points. We show that moduli spaces of arrangements of 10 lines with quadruple points may consist of more than 2 disconnected components, namely 3 or 4 distinct points. We also present defining equations to those arrangements whose moduli spaces are still reducible after taking quotients of complex conjugations. 相似文献
18.
M. Brodmann 《Journal of Pure and Applied Algebra》2011,215(12):2859-184
Let X⊂Pr be a variety of almost minimal degree which is the projected image of a rational normal scroll from a point p outside of . In this paper we study the tangent spaces at singular points of X and the geometry of the embedding scrolls of X, i.e. the rational normal scrolls Y⊂Pr which contain X as a codimension one subvariety. 相似文献
19.
20.
Takeshi Kajiwara 《Archiv der Mathematik》2006,86(1):43-49
We show fundamental properties on embedding of abelian surfaces into projective toric 4-folds, and study the case of the toric
Del Pezzo 4-fold from the viewpoint of the moduli space of abelian surfaces with polarization of type (1, 5).
Received: 31 January 2005; revised: 15 April 2005 相似文献