GW/PT Descendent Correspondence via Vertex Operators

被引：9

作者：

Oblomkov, A. ^{[1
]}

Okounkov, A. ^{[2
,3
,4
]}

Pandharipande, R. ^{[5
]}

机构：

[1] Univ Massachusetts, Dept Math & Stat, Amherst, MA 01003 USA

[2] Columbia Univ, Dept Math, New York, NY 10027 USA

[3] Inst Problems Informat Transmiss, Moscow, Russia

[4] HSE, Lab Representat Theory & Math Phys, Moscow, Russia

[5] Swiss Fed Inst Technol, Dept Math, Zurich, Switzerland

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2020年 / 374卷 / 03期

基金：

俄罗斯科学基金会; 欧洲研究理事会; 美国国家科学基金会;

关键词：

GROMOV-WITTEN THEORY; DONALDSON-THOMAS THEORY; VIRASORO CONSTRAINTS; HILBERT SCHEMES; STABLE PAIRS; CURVES; INVARIANTS; ALGEBRAS;

D O I：

10.1007/s00220-020-03686-4

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We propose an explicit formula for the GW/PT descendent correspondence in the stationary case for nonsingular connected projective threefolds. The formula, written in terms of vertex operators, is found by studying the 1-leg geometry. We prove the proposal for all nonsingular projective toric threefolds. An application to the Virasoro constraints for the stationary descendent theory of stable pairs will appear in a sequel.

引用

页码：1321 / 1359

页数：39

共 43 条

[1] The orbifold DT/PT vertex correspondence
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[2] Gromov-Witten/pairs descendent correspondence for toric 3-folds
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[3] EXTS AND VERTEX OPERATORS
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[9] Vertex operators and quasimodularity of Chern numbers on the Hilbert scheme
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[10] Vertex Operators, Grassmannians, and Hilbert Schemes
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