Stable pairs and Gopakumar-Vafa type invariants for Calabi-Yau 4-folds

被引：19

作者：

Cao, Yalong ^{[1
]}

Maulik, Davesh ^{[2
]}

Toda, Yukinobu ^{[1
]}

机构：

[1] Univ Tokyo, Kavli Inst Phys & Math Univ WPI, Inst Adv Study, Kashiwa, Chiba 2778583, Japan

[2] MIT, Dept Math, 77 Massachusetts Ave, Cambridge, MA 02139 USA

来源：

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2022年 / 24卷 / 02期

关键词：

Stable pairs; Gopakumar-Vafa type invariants; Calabi-Yau; 4-folds; DONALDSON-THOMAS INVARIANTS; GROMOV-WITTEN INVARIANTS; CYCLES;

D O I：

10.4171/JEMS/1110

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

As an analogy to the Gopakumar-Vafa conjecture on CY 3-folds, Klemm-Pandharipande defined GV type invariants on CY 4-folds using GW theory and conjectured their integrality. In this paper, we define stable pair type invariants on CY 4-folds and use them to interpret these GV type invariants. Examples are computed for both compact and non-compact CY 4-folds to support our conjectures.

引用

页码：527 / 581

页数：55

共 43 条

[1] The intrinsic normal cone [J].

Behrend, K ;

Fantechi, B .

INVENTIONES MATHEMATICAE, 1997, 128 (01) :45-88

[2] Symmetric obstruction theories and Hilbert schemes of points on threefolds [J].

Behrend, Kai ;

Fantechi, Barbara .

ALGEBRA & NUMBER THEORY, 2008, 2 (03) :313-345

[3] KODAIRA-SPENCER THEORY OF GRAVITY AND EXACT RESULTS FOR QUANTUM STRING AMPLITUDES [J].

BERSHADSKY, M ;

CECOTTI, S ;

OOGURI, H ;

VAFA, C .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1994, 165 (02) :311-427

[4] Virtual fundamental classes for moduli spaces of sheaves on Calabi-Yau four-folds [J].

Borisov, Dennis ;

Joyce, Dominic .

GEOMETRY & TOPOLOGY, 2017, 21 (06) :3231-3311

[5]

Cao Y., 2020, ARXIV200910909

[6]

Cao Y., 2020, ARXIV190904897

[7]

Cao Y., 2020, ARXIV200409355

[8]

Cao Y., 2015, ARXIV14077659V2

[9] Curve counting and DT/PT correspondence for Calabi-Yau 4-folds [J].

Cao, Yalong ;

Kool, Martijn .

ADVANCES IN MATHEMATICS, 2020, 375

[10] Gopakumar-Vafa Type Invariants on Calabi-Yau 4-Folds via Descendent Insertions [J].

Cao, Yalong ;

Toda, Yukinobu .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2021, 383 (01) :281-310

← 1 2 3 4 5 →