Work

Comparison of nonarchimedean and logarithmic mirror constructions via the Frobenius structure theorem

Year: 2024

Type: article

Abstract: For a log Calabi Yau pair () with smooth affine, satisfying either a maximal degeneracy assumption or contains a Zariski dense torus, we prove under the condition that D is the support of a nef divisor that the structure constants defining a trace form on the mirror algebra constructed by Gross–Siebert are given by the naive curve counts defined by Keel–Yu. As a corollary, we deduce that the equality of the mirror algebras constructed by Gross–Siebert and Keel–Yu in the case contains a Zariski dense torus. In addition, we use this result to prove a mirror conjecture proposed by Mandel for Fano pairs satisfying the maximal degeneracy assumption.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.12998

Author: Samuel Johnston

Institution: Imperial College London

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,780

Funders: Engineering and Physical Sciences Research Council, European Research Council