Toric degenerations of spherical varieties

被引：45

作者：

Alexeev V. ^{[1
]}

Brion M. ^{[2
]}

机构：

[1] Department of Mathematics, University of Georgia, Athens, 30602, GA

[2] Institut Fourier, B.P. 74 38402, Saint-Martin d’Hères Cedex

来源：

Selecta Mathematica | 2005年 / 10卷 / 4期

基金：

美国国家科学基金会;

关键词：

Degenerations; Moduli; Spherical varieties; Toric varieties;

D O I：

10.1007/s00029-005-0396-8

中图分类号：

学科分类号：

摘要：

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. © Birkhäuser Verlag, Basel, 2004.

引用

页码：453 / 478

页数：25

共 29 条

[1]

Alexeev V., Brion M., Stable reductive varieties: Affine varieties., Invent. Math, 157, pp. 227-274, (2004)

[2]

Alexeev V., Brion M., Stable reductive varieties: Projective case, Adv. in Math., 184, pp. 380-408, (2004)

[3]

Alexeev V., Brion M., Moduli of affine schemes with reductive group action, J. Algebraic Geom, 14, pp. 83-117, (2005)

[4]

Alexeev V., Log canonical singularities and complete moduli of stable pairs, Preprint, (1996)

[5]

Alexeev V., Higher-Dimensional Complex Varieties (Trento, 1994), pp. 1-22, (1996)

[6]

Alexeev V., Complete moduli in the presence of semiabelian group action, Ann. of Math., 155, 2, pp. 611-708, (2002)

[7]

Batyrev V., Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties, J. Algebraic Geom, 3, pp. 493-535, (1994)

[8]

Batyrev V.V., Ciocan-Fontanine I., Kim B., Van Straten D., Mirror symmetry and toric degenerations of partial flag manifolds, Acta Math, 184, pp. 1-39, (2000)

[9]

Boutot J.-F., Singularit´es rationnelles et quotients par les groupes réductifs. Invent, Math, 88, pp. 65-68, (1987)

[10]

Berenstein A.D., Zelevinsky A.V., Tensor product multiplicities and convex polytopes in partition space, J. Geom. Phys, 5, pp. 453-472, (1988)

← 1 2 3 →