Work

On the Degree of Irrationality of Low Genus $k3$ Surfaces

Year: 2025

Type: article

Abstract: Given a general polarized $K3$ surface $S\subset \mathbb P^g$ of genus $g\le 14$ , we study projections of minimal degree and their variational structure. In particular, we prove that the degree of irrationality of all such surfaces is at most $4$ , and that for $g=7,8,9,11$ there are no rational maps of degree $3$ induced by the primitive linear system. Our methods combine vector bundle techniques à la Lazarsfeld with derived category tools and also make use of the rich theory of singular curves on $K3$ surfaces.

Source: Journal of the Institute of Mathematics of Jussieu

DOI: 10.1017/s1474748024000525

Authors: Federico Moretti, Andrés Rojas

Institutions: Humboldt-Universität zu Berlin, Stony Brook 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: $3,550

Funder: European Commission