Semiorthogonal decompositions in algebraic geometry

被引：0

作者：

Kuznetsov, Alexander ^{[1
,2
,3
]}

机构：

[1] Steklov Math Inst, 8 Gubkin Str, Moscow 119991, Russia

[2] Independent Univ Moscow, Poncelet Lab, Moscow, Russia

[3] SU HSE, Lab Algebra Geometry, Moscow, Russia

来源：

PROCEEDINGS OF THE INTERNATIONAL CONGRESS OF MATHEMATICIANS (ICM 2014), VOL II | 2014年

关键词：

Semiorthogonal decompositions; exceptional collections; Lefschetz decompositions; homological projective duality; categorical resolutions of singularities; Fano varieties; EXCEPTIONAL COLLECTIONS; VECTOR-BUNDLES; COHERENT SHEAVES; CATEGORIES; GRASSMANNIANS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this review we discuss what is known about semiorthogonal decompositions of derived categories of algebraic varieties. We review existing constructions, especially the homological projective duality approach, and discuss some related issues such as categorical resolutions of singularities.

引用

页码：635 / 660

页数：26

共 50 条

[21] ALGEBRAIC GEOMETRY
DIEUDONN.J
ADVANCES IN MATHEMATICS, 1969, 3 (03) : 233 - &
[22] Levi decompositions of a linear algebraic group
George J. Mcninch
Transformation Groups, 2010, 15 : 937 - 964
[23] Cylindrical Algebraic Sub-Decompositions
Wilson, D. J.
Bradford, R. J.
Davenport, J. H.
England, M.
MATHEMATICS IN COMPUTER SCIENCE, 2014, 8 (02) : 263 - 288
[24] COMMUTING LINEAR OPERATORS AND ALGEBRAIC DECOMPOSITIONS
Gover, A. Rod
Silhan, Josef
ARCHIVUM MATHEMATICUM, 2007, 43 (05): : 373 - 387
[25] DIRECT DECOMPOSITIONS OF ATOMISTIC ALGEBRAIC LATTICES
LIBKIN, L
ALGEBRA UNIVERSALIS, 1995, 33 (01) : 127 - 135
[26] Levi decompositions of a linear algebraic group
McNinch, George J.
TRANSFORMATION GROUPS, 2010, 15 (04) : 937 - 964
[27] ON APPROXIMATIONS AND INCIDENCE IN CYLINDRICAL ALGEBRAIC DECOMPOSITIONS
PRILL, D
SIAM JOURNAL ON COMPUTING, 1986, 15 (04) : 972 - 993
[28] ALGEBRAIC DECOMPOSITIONS OF COMMUTATIVE ASSOCIATION SCHEMES
FERGUSON, PA
TURULL, A
JOURNAL OF ALGEBRA, 1985, 96 (01) : 211 - 229
[29] On Minimal and Minimum Cylindrical Algebraic Decompositions
Michel, Lucas
Mathonet, Pierre
Zenaidi, Naim
PROCEEDINGS OF THE 2024 INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION, ISSAC 2024, 2024, : 316 - 323
[30] Needle Decompositions in Riemannian Geometry
Klartag, Bo'az
MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 249 (1180) : I - 77

← 1 2 3 4 5 →