Tropical correspondence for smooth del Pezzo log Calabi-Yau pairs

IF 0.9 1区数学 Q2 MATHEMATICS

Journal of Algebraic Geometry Pub Date : 2020-05-28 DOI:10.1090/jag/794

Tim Graefnitz

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引用次数: 21

Abstract

Consider a log Calabi-Yau pair ( X , D ) (X,D) consisting of a smooth del Pezzo surface X X of degree ≥ 3 \geq 3 and a smooth anticanonical divisor D D . We prove a correspondence between genus zero logarithmic Gromov-Witten invariants of X X intersecting D D in a single point with maximal tangency and the consistent wall structure appearing in the dual intersection complex of ( X , D ) (X,D) from the Gross-Siebert reconstruction algorithm. More precisely, the logarithm of the product of functions attached to unbounded walls in the consistent wall structure gives a generating function for these invariants.

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光滑del Pezzo对数Calabi-Yau对的热带对应关系

考虑一个对数Calabi-Yau对（X，D）（X，D），它由一个≥3次的光滑del Pezzo表面X和一个光滑反正则除数D组成。我们从Gross-Sibert重建算法中证明了在具有最大切点的单点上与D相交的X X的亏格零对数Gromov-Witten不变量与（X，D）（X，D）的对偶交复数中出现的一致壁结构之间的对应关系。更准确地说，在一致墙结构中，附加到无界墙的函数的乘积的对数给出了这些不变量的生成函数。

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来源期刊

Journal of Algebraic Geometry 数学-数学

CiteScore

2.70

自引率

5.60%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Algebraic Geometry is devoted to research articles in algebraic geometry, singularity theory, and related subjects such as number theory, commutative algebra, projective geometry, complex geometry, and geometric topology. This journal, published quarterly with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.