English

Algebraic cycles and special Horikawa surfaces

Algebraic Geometry 2020-09-25 v1

Abstract

This note is about a 1616-dimensional family of surfaces of general type with pg=2p_g=2 and q=0q=0 and K2=1K^2=1, called "special Horikawa surfaces". These surfaces, studied by Pearlstein-Zhang and by Garbagnati, are related to K3 surfaces. We show that special Horikawa surfaces have a multiplicative Chow-K\"unneth decomposition, in the sense of Shen-Vial. As a consequence, the Chow ring of special Horikawa surfaces displays K3-like behaviour.

Keywords

Cite

@article{arxiv.2009.11634,
  title  = {Algebraic cycles and special Horikawa surfaces},
  author = {Robert Laterveer},
  journal= {arXiv preprint arXiv:2009.11634},
  year   = {2020}
}

Comments

15 pages, to appear in Acta Math. Vietnamica, comments welcome

R2 v1 2026-06-23T18:45:56.728Z