Beilinson's conjecture on K3 surfaces with an involution

TL;DR

This paper proves Beilinson's conjecture for specific K3 surfaces with involution, where the quotient surface is a projective plane branched along a sextic, advancing understanding of algebraic cycles on K3 surfaces.

Contribution

It establishes the validity of Beilinson's conjecture for a new class of K3 surfaces with involution, linking geometric properties to conjectural algebraic cycle behavior.

Findings

Beilinson's conjecture verified for certain K3 surfaces with involution

The quotient surface is a projective plane branched along a sextic

Provides new evidence supporting Beilinson's conjecture in algebraic geometry

Abstract

In this note we prove that the Beilinson conjecture holds for certain examples of K3 surfaces over $\bar {\mathbb{Q}}$ equipped with an involution, when the quotient of the surface by the involution is the projective plane branched along a sextic.