A stratification of $$B^4(2,K_C)$$B4(2,KC) over a general curve

Abstract

Let C be a smooth curve of genus $$g\ge 10$$ with general moduli. We show that the Brill–Noether locus $$B^4(2,K_C)$$ contains irreducible subvarieties $${\mathcal {B}}_3\supset {\mathcal {B}}_4\supset \cdots \supset {\mathcal {B}}_n$$, where each $${\mathcal {B}}_k$$ has dimension $$3g-10-k$$ and $${\mathcal {B}}_3$$ is an irreducible component of the expected dimension the Brill–Noether number $$\rho =3g-13$$.