共查询到20条相似文献,搜索用时 0 毫秒
1.
We prove that any affine, resp. polarized projective, spherical variety admits a flat degeneration to an affine, resp. polarized projective, toric variety. Motivated by mirror symmetry, we give conditions for the limit toric variety to be a Gorenstein Fano, and provide many examples. We also provide an explanation for the limits as boundary points of the moduli space of stable pairs whose existence is predicted by the Minimal Model Program. 相似文献
2.
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
3.
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
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.
We give explicit formulas for the dimensions and the degrees of A-discriminant varieties introduced by Gelfand, Kapranov and Zelevinsky. Our formulas can be applied also to the case where the A-discriminant varieties are higher-codimensional and their degrees are described by the geometry of the configurations A. Moreover combinatorial formulas for the Euler obstructions of general (not necessarily normal) toric varieties will be also given. 相似文献
6.
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
7.
Annette A’Campo–Neuen 《Archiv der Mathematik》2006,87(3):217-226
We prove tight lower bounds for the coefficients of the toric h-vector of an arbitrary centrally symmetric polytope generalizing previous results due to R. Stanley and the author using
toric varieties. Our proof here is based on the theory of combinatorial intersection cohomology for normal fans of polytopes
developed by G. Barthel, J.-P. Brasselet, K. Fieseler and L. Kaup, and independently by P. Bressler and V. Lunts. This theory
is also valid for nonrational polytopes when there is no standard correspondence with toric varieties. In this way we can
establish our bounds for centrally symmetric polytopes even without requiring them to be rational.
Received: 24 March 2004 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.
Let X be a complete toric variety and Y a smooth projective variety with . We prove that, if is a surjective morphism then .
Received: 15 May 2001; in final form: 22 October 2001/ Published online: 4 April 2002 相似文献
10.
Nathan Owen Ilten 《Journal of Pure and Applied Algebra》2009,213(6):1086-1096
In the case of two-dimensional cyclic quotient singularities, we classify all one-parameter toric deformations in terms of certain Minkowski decompositions introduced by Altmann [Minkowski sums and homogeneous deformations of toric varieties, Tohoku Math. J. (2) 47 (2) (1995) 151-184.]. In particular, we show how to induce each deformation from a versal family, describe exactly to which reduced versal base space components each such deformation maps, describe the singularities in the general fibers, and construct the corresponding partial simultaneous resolutions. 相似文献
11.
Ivan Soprunov 《Journal of Pure and Applied Algebra》2007,209(2):383-392
We consider families of sparse Laurent polynomials f1,…,fn with a finite set of common zeros Zf in the torus Tn=(C−{0})n. The global residue assigns to every Laurent polynomial g the sum of its Grothendieck residues over Zf. We present a new symbolic algorithm for computing the global residue as a rational function of the coefficients of the fi when the Newton polytopes of the fi are full-dimensional. Our results have consequences in sparse polynomial interpolation and lattice point enumeration in Minkowski sums of polytopes. 相似文献
12.
A classification of toric varieties with few generators 总被引:3,自引:0,他引:3
Peter Kleinschmidt 《Aequationes Mathematicae》1988,35(2-3):254-266
13.
Enrique Reyes 《Advances in Applied Mathematics》2012,48(1):64-78
Let IG be the toric ideal of a graph G. We characterize in graph theoretical terms the primitive, the minimal, the indispensable and the fundamental binomials of the toric ideal IG. 相似文献
14.
15.
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
16.
Toric varieties,lattice points and Dedekind sums 总被引:8,自引:0,他引:8
James E. Pommersheim 《Mathematische Annalen》1993,295(1):1-24
17.
We show that Fourier transforms on the Weyl algebras have a geometric counterpart in the framework of toric varieties, namely
they induce isomorphisms between twisted rings of differential operators on regular toric varieties, whose fans are related
to each other by reflections of one-dimensional cones. The simplest class of examples is provided by the toric varieties related
by such reflections to projective spaces. It includes the blow-up at a point of the affine space and resolution of singularities
of varieties appearing in the study of the minimal orbit of
. 相似文献
19.
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
20.
Luis Fuentes García 《Archiv der Mathematik》2005,85(5):409-418
We reduce the problem of the projective normality of polarized abelian varieties to check the rank of very explicit matrices.
This allows us to prove some results on normal generation of primitive line bundles on abelian threefolds and fourfolds. We
also give two situations where the projective normality always fails. Finally we make some conjecture.
Received: 1 September 2004; revised: 10 March 2005 相似文献