An stratification of $B^4(2,K_C)$ over a general curve

TL;DR

This paper investigates the structure of the Brill-Noether locus $B^4(2,K_C)$ for a general curve of genus at least 10, revealing a nested stratification of irreducible subvarieties with specific dimensions.

Contribution

It introduces a detailed stratification of $B^4(2,K_C)$, identifying a hierarchy of irreducible subvarieties with explicit dimensions for general curves.

Findings

Existence of nested irreducible subvarieties within $B^4(2,K_C)$

Dimensions of these subvarieties follow a specific decreasing pattern

The top stratum $B_3$ has the expected dimension $3g-13"

Abstract

For a general curve C of genus $g\geq 10$, we show that the Brill- Noether locus $B^4(2,K_C)$ contains irreducible sub-varieties $B_3\supset B_4 \supset \cdots \supset B_n$, where $B_n$ is of dimension $3g-10-n$ and $B_3$ is an irreducible component of the expected dimension $3g-13$.