ON THE DEGREE OF IRRATIONALITY OF LOW GENUS K3 SURFACES

Federico Moretti; Andrés Rojas

doi:10.1017/S1474748024000525

ON THE DEGREE OF IRRATIONALITY OF LOW GENUS K3 SURFACES

Federico Moretti
, Andrés Rojas

Mathematics

Humboldt University of Berlin

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Given a general polarized K3 surface S ⊂ P^g of genus g ≤ 14, we study projections S →͑ P^g -→ P² 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 S -→ P² 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.

Original language	English
Pages (from-to)	627-662
Number of pages	36
Journal	Journal of the Institute of Mathematics of Jussieu
Volume	24
Issue number	3
DOIs	https://doi.org/10.1017/S1474748024000525
State	Published - May 1 2025

Keywords

Bridgeland stability
Fourier–Mukai transforms
K 3 surfaces
degree of irrationality
kernel bundle

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10.1017/S1474748024000525

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title = "ON THE DEGREE OF IRRATIONALITY OF LOW GENUS K3 SURFACES",

abstract = "Given a general polarized K3 surface S ⊂ Pg of genus g ≤ 14, we study projections S →͑ Pg -→ P2 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 S -→ P2 of degree 3 induced by the primitive linear system. Our methods combine vector bundle techniques {\`a} la Lazarsfeld with derived category tools and also make use of the rich theory of singular curves on K3 surfaces.",

keywords = "Bridgeland stability, Fourier–Mukai transforms, K 3 surfaces, degree of irrationality, kernel bundle",

author = "Federico Moretti and Andr{\'e}s Rojas",

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year = "2025",

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language = "English",

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T1 - ON THE DEGREE OF IRRATIONALITY OF LOW GENUS K3 SURFACES

AU - Moretti, Federico

AU - Rojas, Andrés

N1 - Publisher Copyright: © The Author(s), 2025.

PY - 2025/5/1

Y1 - 2025/5/1

N2 - Given a general polarized K3 surface S ⊂ Pg of genus g ≤ 14, we study projections S →͑ Pg -→ P2 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 S -→ P2 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.

AB - Given a general polarized K3 surface S ⊂ Pg of genus g ≤ 14, we study projections S →͑ Pg -→ P2 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 S -→ P2 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.

KW - Bridgeland stability

KW - Fourier–Mukai transforms

KW - K 3 surfaces

KW - degree of irrationality

KW - kernel bundle

UR - https://www.scopus.com/pages/publications/105002680960

U2 - 10.1017/S1474748024000525

DO - 10.1017/S1474748024000525

M3 - Article

AN - SCOPUS:105002680960

SN - 1474-7480

VL - 24

SP - 627

EP - 662

JO - Journal of the Institute of Mathematics of Jussieu

JF - Journal of the Institute of Mathematics of Jussieu

IS - 3

ER -

ON THE DEGREE OF IRRATIONALITY OF LOW GENUS K3 SURFACES

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Keywords

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