The polarized degree of irrationality of K3 surfaces

2023/03/13 by Federico Moretti, Moretti, Federico · 4 citations
Mathematics · #Algebraic Geometry and Number Theory #Advanced Differential Equations and Dynamical Systems #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2303.07289

Abstract

Given a polarized variety (X,L), we construct and study projections of low degree X\dashrightarrow ℙ(H⁰(L^\vee)) \dashrightarrow \mathbb P ⁿ using the associated kernel bundles. As an application, we can show that the degree of irrationality of a very general (1,6)-polarized abelian surface, as well as that of a very general K3 surface of genus 6 is 3. We also give new upper bounds on the degree of irrationality of K3 surfaces of any genus. We study the family of projections of minimal degree of a very general K3 surface of genus 4,5,6. As a different application of our construction, we exhibit new generically finite rational maps of low degree from some hyper-Kähler varieties and abelian varieties to projective spaces.

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