Quantum mirrors of log Calabi-Yau surfaces and higher-genus curve counting

被引：13

作者：

Bousseau, Pierrick ^{[1
,2
]}

机构：

[1] Imperial Coll London, Dept Math, London SW7 2AZ, England

[2] Swiss Fed Inst Technol, Inst Theoret Studies, CH-8092 Zurich, Switzerland

来源：

COMPOSITIO MATHEMATICA | 2020年 / 156卷 / 02期

基金：

英国工程与自然科学研究理事会;

关键词：

mirror symmetry; deformation quantization; Gromov-Witten invariants; STABLE LOGARITHMIC MAPS; DEFORMATION QUANTIZATION; GEOMETRY; VARIETIES; SYMMETRY; DUALITY; MODULI;

D O I：

10.1112/S0010437X19007760

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Gross, Hacking and Keel have constructed mirrors of log Calabi-Yau surfaces in terms of counts of rational curves. Using q-deformed scattering diagrams defined in terms of higher-genus log Gromov-Witten invariants, we construct deformation quantizations of these mirrors and we produce canonical bases of the corresponding non-commutative algebras of functions.

引用

页码：360 / 411

页数：52

共 51 条

[1] LAGRANGIAN FIBRATIONS ON BLOWUPS OF TORIC VARIETIES AND MIRROR SYMMETRY FOR HYPERSURFACES [J].