Work

Mirror symmetry and rigid structures of generalized K3 surfaces

Year: 2024

Type: article

Abstract: The present article is concerned with mirror symmetry for generalized K3 surfaces, with particular emphasis on complex and Kähler rigid structures. Inspired by the works of Dolgachev, Aspinwall–Morrison and Huybrechts, we introduce a formulation of mirror symmetry for generalized K3 surfaces by using Mukai lattice polarizations. This approach solves issues in the conventional formulations of mirror symmetry for K3 surfaces. In particular, we provide a solution to the problem of mirror symmetry for singular K3 surfaces. Along the way, we investigate complex and Kähler rigid structures of generalized K3 surfaces.

Source: Advances in Mathematics

DOI: 10.1016/j.aim.2024.110050

Author: Atsushi Kanazawa

Institution: Waseda University

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,510

Funder: Japan Society for the Promotion of Science