共查询到20条相似文献,搜索用时 15 毫秒
1.
Benoit Bertrand 《Geometriae Dedicata》2006,118(1):49-70
A real algebraic variety is maximal (with respect to the Smith-Thom inequality) if the sum of the Betti numbers (with
coefficients) of the real part of the variety is equal to the sum of Betti numbers of its complex part. We prove that there exist polytopes that are not Newton polytopes of any maximal hypersurface in the corresponding toric variety. On the other hand we show that for any polytope Δ there are families of hypersurfaces with the Newton polytopes
that are asymptotically maximal when λ tends to infinity. We also show that these results generalize to complete intersections. 相似文献
2.
Mathematical Notes - Criteria for the flexibility, rigidity, and almost rigidity of nonnormal affine toric varieties are obtained. For rigid and almost rigid toric varieties, automorphism groups... 相似文献
3.
We study the Lie algebra of derivations of the coordinate ring of affine toric varieties defined by simplicial affine semigroups and prove the following results:Such toric varieties are uniquely determined by their Lie algebra if they are supposed to be Cohen–Macaulay of dimension 2 or Gorenstein of dimension =1.In the Cohen–Macaulay case, every automorphism of the Lie algebra is induced from a unique automorphism of the variety.Every derivation of the Lie algebra is inner. 相似文献
4.
Hu 《Discrete and Computational Geometry》2008,28(2):151-174
Abstract. For linear projections of polytopes and fans of cones we introduce some new objects such as: virtual chambers, virtual cones
and (locally) coherent costrings. Virtual chambers (cones) generalize real chambers (cones), while (locally) coherent costrings
are linear dual to (locally) coherent strings. We establish various correspondences for these objects and their connections
to toric geometry. 相似文献
5.
We prove Sturmfels' conjecture that toric varieties of codimension two have no other flat deformations than those obtained by Gröbner basis theory. 相似文献
6.
7.
Hu 《Discrete and Computational Geometry》2002,28(2):151-174
Abstract. For linear projections of polytopes and fans of cones we introduce some new objects such as: virtual chambers, virtual cones and (locally) coherent costrings. Virtual chambers (cones) generalize real chambers (cones), while (locally) coherent costrings are linear dual to (locally) coherent strings. We establish various correspondences for these objects and their connections to toric geometry. 相似文献
8.
Joseph Gubeladze 《K-Theory》2003,28(4):285-327
A natural higher K-theoretic analogue of the triviality of vector bundles on affine toric varieties is the conjecture on nilpotence of the multiplicative action of the natural numbers on the K-theory of these varieties. This includes both Quillen's fundamental result on K-homotopy invariance of regular rings and the stable version of the triviality of vector bundles on affine toric varieties. Moreover, it yields a similar behavior of not necessarily affine toric varieties and, further, of their equivariant closed subsets. The conjecture is equivalent to the claim that the relevant admissible morphisms of the category of vector bundles on an affine toric variety can be supported by monomials not in a nondegenerate corner subcone of the underlying polyhedral cone. We prove that one can in fact eliminate all lattice points in such a subcone, except maybe one point. The elimination of the last point is also possible in 0 characteristic if the action of the big Witt vectors satisfies a very natural condition. A partial result of this in the arithmetic case provides first nonsimplicial examples, actually an explicit infinite series of combinatorially different affine toric varieties, simultaneously verifying the conjecture for all higher groups.Supported by the Deutsche Forschungsgemeinschaft, INTAS grant 99-00817 and TMR grant ERB FMRX CT-97-0107 相似文献
9.
It is proved that under certain conditions the group K
n
(X) of a smooth projective variety X over a field F is a natural direct summand of K
n
(A) for some separable F-algebra A. As an application we study the K-groups of toric models and toric varieties. A presentation in terms of generators and relations of the groupK
0(T) for an algebraic torus T is given. 相似文献
10.
Letitia Golubitsky 《代数通讯》2013,41(6):2091-2105
It is well known that the Eulerian polynomials, which count permutations in S n by their number of descents, give the h-polynomial/h-vector of the simple polytopes known as permutohedra, the convex hull of the S n -orbit for a generic weight in the weight lattice of S n . Therefore, the Eulerian polynomials give the Betti numbers for certain smooth toric varieties associated with the permutohedra. In this article we derive recurrences for the h-vectors of a family of polytopes generalizing this. The simple polytopes we consider arise as the orbit of a nongeneric weight, namely, a weight fixed by only the simple reflections J = {s n , s n?1, s n?2,…, s n?k+2, s n?k+1} for some k with respect to the A n root lattice. Furthermore, they give rise to certain rationally smooth toric varieties X(J) that come naturally from the theory of algebraic monoids. Using effectively the theory of reductive algebraic monoids and the combinatorics of simple polytopes, we obtain a recurrence formula for the Poincaré polynomial of X(J) in terms of the Eulerian polynomials. 相似文献
11.
Ionut Ciocan-Fontanine 《Transactions of the American Mathematical Society》1999,351(7):2695-2729
We describe the small quantum cohomology ring of complete flag varieties by algebro-geometric methods, as presented in our previous work Quantum cohomology of flag varieties (Internat. Math. Res. Notices, no. 6 (1995), 263-277). We also give a geometric proof of the quantum Monk formula.
12.
N. A. Bushueva 《Siberian Mathematical Journal》2010,51(5):776-788
In ℂn we consider an algebraic surface Y and a finite collection of hypersurfaces Si. Froissart’s theorem states that if Y and Si are in general position in the projective compactification of ℂn together with the hyperplane at infinity then for the homologies of Y \∪ Si we have a special decomposition in terms of the homology of Y and all possible intersections of Si in Y. We prove the validity of this homological decomposition on assuming a weaker condition: there exists a smooth toric
compactification of ℂn in which Y and Si are in general position with all divisors at infinity. One of the key steps of the proof is the construction of an isotopy
in Y leaving invariant all hypersurfaces Y ∩ Sk with the exception of one Y ∩ Si, which is shifted away from a given compact set. Moreover, we consider a purely toric version of the decomposition theorem,
taking instead of an affine surface Y the complement of a surface in a compact toric variety to a collection of hypersurfaces
in it. 相似文献
13.
In this paper we apply the results of [W] on the twisted Mellin transform to problems in toric geometry. In particular, we use these results to describe the asymptotics of probability densities associated with the monomial eigenstates, z k , $ k \in \mathbb{Z}^{d} $ , in Bargmann space and prove an “upstairs” version of the spectral density theorem of [BGU]. We also obtain for the z k ’s, “upstairs” versions of the results of [STZ] on distribution laws for eigenstates on toric varieties. 相似文献
14.
Marcel Morales 《代数通讯》2013,41(8):2409-2430
In this article we prove the following:
-
Some results on the Cohen–Macaulayness of the canonical module;
-
We study the S 2-fication of rings which are quotients by lattices ideals;
-
Given a simplicial lattice ideal of codimension two I, its Macaulayfication is given explicitly from a system of generators of I.
15.
David G. Wagner 《Journal of Algebraic Combinatorics》1996,5(2):149-165
With each finite lattice L we associate a projectively embedded scheme V(L); as Hibi has shown, the lattice D is distributive if and only if V(D) is irreducible, in which case it is a toric variety. We first apply Birkhoff's structure theorem for finite distributive lattices to show that the orbit decomposition of V(D) gives a lattice isomorphic to the lattice of contractions of the bounded poset of join-irreducibles
of D. Then we describe the singular locus of V(D) by applying some general theory of toric varieties to the fan dual to the order polytope of P: V(D) is nonsingular along an orbit closure if and only if each fibre of the corresponding contraction is a tree. Finally, we examine the local rings and associated graded rings of orbit closures in V(D). This leads to a second (self-contained) proof that the singular locus is as described, and a similar combinatorial criterion for the normal link of an orbit closure to be irreducible. 相似文献
16.
《代数通讯》2013,41(8):3735-3752
Abstract In this paper we give an explicit formula for the Riemann-Roch map for singular schemes which are quotients of smooth schemes by diagonalizable groups. As an application we obtain a simple proof of a formula for the Todd class of a simplicial toric variety. An equivariant version of this formula was previously obtained for complete simplicial toric varieties by Brion and Vergne (Brion M. and Vergne M. ([1997]). An equivariant Riemann-Roch theorem for complete simplicial toric varieties. J. Reine. Agnew. Math.482:67–92) using different techniques. 相似文献
17.
We prove that the simplicial complex Ω
n
of chains of matroids (with respect to the ordering by the quotient relation) on n elements is shellable. This follows from a more general result on shellability of the simplicial complex of W -matroids for an arbitrary finite Coxeter group W , and generalises the well-known results by Solomon—Tits and Bj?rner on spherical buildings.
Received January 16, 2000, and in revised form October 7, 2000, and April 16, 2001. Online publication December 21, 2001. 相似文献
18.
19.
Jen-Chieh Hsiao 《代数通讯》2013,41(5):1618-1624
We construct a 3-dimensional complete intersection toric variety on which the subadditivity formula doesn't hold, answering negatively a question by Takagi and Watanabe. A combinatorial proof of the subadditivity formula on 2-dimensional normal toric varieties is also provided. 相似文献
20.
J. Matthew Douglass 《Mathematische Nachrichten》1998,189(1):107-120
Suppose G is a connected reductive algebraic group, P is a parabolic subgroup of G, L is a Levi factor of P, and e is a regular nilpotent element in Lie L. We assume that the characteristic of the underlying field is good for G. Choose a maximal torus, T, and a Borel subgroup, B, of G, so that T?B∩L, B ? P and e ∈ Lie B. Let β be the variety of Borel subgroups of G and let ??e be the subset of ?? consisting of Borel subgroups whose Lie algebras contain e. Finally, let W be the Weyl group of G with respect to T. For ω ∈ W let ??ω be the B-orbit in ?? containing ωB. We consider the intersections ??ω ∩ ??e. The main result is that if dim ??ω ∩ ??e = dim ??e, then ??ω ∩ ??e is an affine space. Thus, the irreducible components of ??e are indexed by Weyl group elements. It is also shown that if G is of type A, then this set of Weyl group elements is a right cell in W. 相似文献