Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Chow ring of moduli spaces of quasi-polarised K3 surfaces in lower genus

Fei Si

Abstract

In the paper, we show the Chow ring of moduli spaces of quasi-polarised K3 surfaces in lower genus ($\le 5$) is tautological.

Chow ring of moduli spaces of quasi-polarised K3 surfaces in lower genus

Abstract

In the paper, we show the Chow ring of moduli spaces of quasi-polarised K3 surfaces in lower genus () is tautological.
Paper Structure (17 sections, 20 theorems, 41 equations, 2 tables)

This paper contains 17 sections, 20 theorems, 41 equations, 2 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Equivaraint Chow ring
  4. K3 surface in lower genus and their moduli
  5. $g=3$ case
  6. $g=4$ and $g=5$ case
  7. Tautological rings and Noether-Lefchetz locus
  8. Chow ring of lattice quasi-polarised K3 surfaces
  9. Chow ring of open part
  10. $g=3$ case
  11. $g=4$ case
  12. $g=5$ case
  13. Chow ring of NL divisors $\mathop{\mathrm{\mathrm{P}}}\nolimits_{d,1}^g$.
  14. Unigonal divisor
  15. Chow ring of hyperelliptic divisor
  16. ...and 2 more sections

Key Result

Theorem 1.1

The Chow ring $A^\ast({\mathcal{F}}_g)$ is tautological, i.e, $A^\ast({\mathcal{F}}_g)=R^\ast({\mathcal{F}}_g)$ for $g \le 5$.

Theorems & Definitions (40)

  • Theorem 1.1
  • Remark 1.2
  • Theorem 1.3
  • Conjecture 1.4
  • Remark 1.5
  • Definition 2.1
  • Remark 2.2
  • Proposition 2.3
  • Remark 2.4
  • Proposition 2.5
  • ...and 30 more