Weierstrass cycles and tautological rings in various moduli spaces of algebraic curves

TL;DR

This paper investigates Weierstrass cycles and tautological rings within various moduli spaces of algebraic curves, providing formulas and estimates especially for curves of genus up to 6.

Contribution

It introduces a general formula for estimating the dimension of Weierstrass cycles in low-genus moduli spaces of algebraic curves.

Findings

The formula accurately estimates Weierstrass cycle dimensions for genus ≤ 6.

Analysis of tautological rings in different moduli spaces.

Enhanced understanding of geometric properties of algebraic curves.

Abstract

We analyze Weierstrass cycles and tautological rings in moduli space of smooth algebraic curves and in moduli spaces of integral algebraic curves with embedded disks with special attention to moduli spaces of curves having genus $\leq 6$. In particular, we show that our general formula gives a good estimate for the dimension of Weierstrass cycles for lower genera.