The tropical superpotential for P2

被引：5
|
作者：
Prince, Thomas [1 ,2 ]
机构：
[1] Imperial Coll London, Dept Math, 180 Queens Gate, London SW7 2AZ, England
[2] Univ Oxford, Math Inst, Woodstock Rd, Oxford OX2 6GG, England
来源：
ALGEBRAIC GEOMETRY | 2020年 / 7卷 / 01期
基金：
英国工程与自然科学研究理事会;
关键词：
mirror symmetry; affine geometry; del Pezzo surfaces; MIRROR SYMMETRY; TORIC VARIETIES; GEOMETRY; SURFACES;
D O I：
10.14231/AG-2020-002
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We present an extended worked example of the computation of the tropical superpotential considered by Carl-Pumperla-Siebert. In particular, we consider an affine manifold associated with the complement of a non-singular genus 1 plane curve and calculate the wall-and-chamber decomposition determined by the Gross-Siebert algorithm. Using the results of Carl-Pumperla-Siebert, we determine the tropical superpotential, via broken line counts, in every chamber of this decomposition. The superpotential defines a Laurent polynomial in every chamber, and we show that these are precisely the Laurent polynomials predicted by Coates-Corti-Galkin-Golyshev-Kaspzryk to be mirror to P-2
引用
收藏
页码：30 / 58
页数：29
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