Derived Category of Equivariant Coherent Sheaves on a Smooth Toric Variety and Koszul Duality

被引：0
作者：
Valery Lunts [1 ]
机构：
[1] Department of Mathematics, Indiana University, Bloomington, IN
[2] National Research University Higher School of Economics, Moscow
来源：
Functional Analysis and Its Applications | 2025年 / 59卷 / 1期
关键词：
derived category; equivariant coherent sheaves; toric varieties;
D O I：
10.1134/S1234567825010057
中图分类号：
学科分类号：
摘要：
Abstract: Let be a smooth toric variety defined by the fan. We consider as a finite set with topology and define a natural sheaf of graded algebras on. The category of modules over is studied (together with other related categories). This leads to a certain combinatorial Koszul duality equivalence. We describe the equivariant category of coherent sheaves and a related (slightly bigger) equivariant category in terms of sheaves of modules over the sheaf of algebras. Eventually (for a complete), the combinatorial Koszul duality is interpreted in terms of the Serre functor on. © Pleiades Publishing, Ltd. 2025.
引用
收藏
页码：38 / 64
页数：26
相关论文
共 8 条
  • [1] Atiyah M.F., Macdonald I.G., Introduction to commutative algebra, (1969)
  • [2] Bernstein J., Lunts V., Equivariant sheaves and functors, 1578, (1994)
  • [3] Braden T., Lunts V.A., Equivariant-constructible Koszul duality for dual toric varieties, Adv. Math, 201, 2, pp. 408-453, (2006)
  • [4] Danilov V.I., The geometry of toric varieties, Russian Math. Surveys, 33, 2, pp. 97-154, (1978)
  • [5] Fulton W., Introduction to toric varieties, 131, (1993)
  • [6] Godement R., Topologie algébrique et théorie des faisceaux, 13, (1958)
  • [7] Kempf G., The Grothendieck–Cousin complex of an induced representation, Adv. Math, 29, 3, pp. 310-396, (1978)
  • [8] Lunts V., Equivariant sheaves on toric varieties, Compos. Math, 96, 1, pp. 63-83, (1995)
1