ATOMIC OBJECTS ON HYPER-KAHLER MANIFOLDS

被引：0

作者：

Beckmann, Thorsten ^{[1
]}

机构：

[1] Max Planck Inst Math, Vivatsgasse 7, D-53111 Bonn, Germany

来源：

JOURNAL OF ALGEBRAIC GEOMETRY | 2024年

关键词：

COMPACT HYPERKAHLER MANIFOLDS; MODULI SPACES; K3; SURFACES; FORMALITY; SHEAVES; SINGULARITIES; EQUIVALENCES; DEFORMATIONS; CONJECTURE; COHOMOLOGY;

D O I：

10.1090/jag/830

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce and study the notion of atomic sheaves and complexes on higher-dimensional hyper-K & auml;hler manifolds and show that they share many of the intriguing properties of simple sheaves on K3 surfaces. For example, we prove formality of the dg algebra of derived endomorphisms for stable atomic bundles. We further demonstrate the characteristics of atomic objects by studying atomic Lagrangian submanifolds. In the appendix, we prove nonexistence results for spherical objects on hyperKa<spacing diaeresis>hler manifolds.

引用

页数：52

共 50 条

[1] Hyper-Kahler Manifolds
Debarre, Olivier
[J]. MILAN JOURNAL OF MATHEMATICS, 2022, 90 (02) : 305 - 387
[2] Hyper-Kahler manifolds
Dancer, AS
[J]. JOURNAL OF DIFFERENTIAL GEOMETRY, 1999, : 15 - 38
[3] On the cohomology of Kahler and hyper-Kahler manifolds
Salamon, SM
[J]. TOPOLOGY, 1996, 35 (01) : 137 - 155
[4] Conification of Kahler and Hyper-Kahler Manifolds
Alekseevsky, D. V.
Cortes, V.
Mohaupt, T.
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2013, 324 (02) : 637 - 655
[5] ON TORIC HYPER-KAHLER MANIFOLDS GIVEN BY THE HYPER-KAHLER QUOTIENT METHOD
GOTO, R
[J]. INTERNATIONAL JOURNAL OF MODERN PHYSICS A, 1992, 7 : 317 - 338
[6] On hyper-Kahler manifolds of type A∞ and D∞
Goto, R
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1998, 198 (02) : 469 - 491
[7] REMARKS ON DEGENERATIONS OF HYPER-KAHLER MANIFOLDS
Kollar, Janos
Laza, Radu
Sacca, Giulia
Voisin, Claire
[J]. ANNALES DE L INSTITUT FOURIER, 2018, 68 (07) : 2837 - 2882
[8] Hyper-Kahler manifolds and multiply intersecting branes
Gauntlett, JP
Gibbons, GW
Papadopoulos, G
Townsend, PK
[J]. NUCLEAR PHYSICS B, 1997, 500 (1-3) : 133 - 162
[9] Twister spaces for hyper-Kahler manifolds with torsion
Howe, PS
Papadopoulos, G
[J]. PHYSICS LETTERS B, 1996, 379 (1-4) : 80 - 86
[10] DECOMPOSITION OF THE EXTERIOR ALGEBRA OF HYPER-KAHLER MANIFOLDS
BONAN, E
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1995, 320 (04): : 457 - 462

← 1 2 3 4 5 →