Formality conjecture for K3 surfaces

被引：10

作者：

Budur, Nero ^{[1
]}

Zhang, Ziyu ^{[2
]}

机构：

[1] Katholieke Univ Leuven, Celestijnenlaan 200B, B-3001 Leuven, Belgium

[2] Leibniz Univ Hannover, Inst Algebra Geometrie, Welfengarten 1, D-30167 Hannover, Germany

来源：

COMPOSITIO MATHEMATICA | 2019年 / 155卷 / 05期

关键词：

K3; surfaces; stable sheaves; formality; DG algebras; DG enhancements; MODULI SPACES; STABILITY CONDITIONS; BIRATIONAL GEOMETRY; SHEAVES; REPRESENTATIONS; SINGULARITIES;

D O I：

10.1112/S0010437X19007206

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a proof of the formality conjecture of Kaledin and Lehn: on a complex projective K3 surface, the differential graded (DG) algebra RHom(center dot) (F; F) is formal for any sheaf F polystable with respect to an ample line bundle. Our main tool is the uniqueness of the DG enhancement of the bounded derived category of coherent sheaves. We also extend the formality result to derived objects that are polystable with respect to a generic Bridgeland stability condition.

引用

页码：902 / 911

页数：10

共 30 条

[1] Singularities of moduli spaces of sheaves on K3 surfaces and Nakajima quiver varieties [J].

Arbarello, E. ;

Sacca, G. .

ADVANCES IN MATHEMATICS, 2018, 329 :649-703

[2] MMP for moduli of sheaves on K3s via wall-crossing: nef and movable cones, Lagrangian fibrations [J].

Bayer, Arend ;

Macri, Emanuele .

INVENTIONES MATHEMATICAE, 2014, 198 (03) :505-590

[3] PROJECTIVITY AND BIRATIONAL GEOMETRY OF BRIDGELAND MODULI SPACES [J].

Bayer, Arend ;

Macri, Emanuele .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2014, 27 (03) :707-752

[4]

Bellamy G., 2016, ARXIV160200164MATHAG

[5] Lectures on DG-Categories [J].

Bertrand, Toen .

TOPICS IN ALGEBRAIC AND TOPOLOGICAL K-THEORY, 2011, 2008 :243-302

[6] ENHANCED TRIANGULATED CATEGORIES [J].

BONDAL, AI ;

KAPRANOV, MM .

MATHEMATICS OF THE USSR-SBORNIK, 1991, 70 (01) :93-107

[7] Stability conditions on K3 surfaces [J].

Bridgeland, Tom .

DUKE MATHEMATICAL JOURNAL, 2008, 141 (02) :241-291

[8]

Budur N., 2018, ARXIV180905180MATHAG

[9]

Budur N., 2018, ARXIV180303974V3MATH

[10] REAL HOMOTOPY THEORY OF KAHLER MANIFOLDS [J].

DELIGNE, P ;

GRIFFITHS, P ;

MORGAN, J ;

SULLIVAN, D .

INVENTIONES MATHEMATICAE, 1975, 29 (03) :245-274

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