# Effective divisors in the projectivized Hodge bundle

## TL;DR

This paper computes the class of a specific divisor locus in the projectivized Hodge bundle related to Weierstrass points and shows certain strata generate extremal rays of pseudoeffective cones.

## Contribution

It provides explicit calculations of divisor classes and demonstrates the extremality of certain strata in the pseudoeffective cones of canonical and bicanonical divisors.

## Key findings

- Computed the class of the closure of the locus of canonical divisors with a zero at a Weierstrass point.
- Showed that strata of canonical and bicanonical divisors with a double zero span extremal rays.
- Established new geometric properties of divisor strata in the Hodge bundle context.

## Abstract

We compute the class of the closure of the locus of canonical divisors in the projectivization of the Hodge bundle $\mathbb{P}\overline{\mathcal{H}}_g$ over $\overline{\mathcal{M}}_g$ which have a zero at a Weierstrass point. We also show that the strata of canonical and bicanonical divisors with a double zero span extremal rays of the respective pseudoeffective cones.