V. Strehl | Search arXiv

arXiv2015

Non-emptiness of Brill-Noether loci in M(2,L)

Let $C$ be a smooth projective complex curve of genus $g \geq 2$. We investigate the Brill-Noether locus consisting of stable bundles of rank 2 and determinant $L$ of odd degree $d$ having at least $k$ independent sections. This locus possesses a virtual fundamental class. We show that in many cases this class is non-zero, which implies that the Brill-Noether locus is non-empty. For many values of $d$ and $k$ the result is best possible. We obtain more precise results for $k\le5$. An appendix contains the proof of a combinatorial lemma which we need.

math.AG↗

arXiv2007

Correspondences with split polynomial equations

We introduce endomorphisms of special jacobians and show that they satisfy polynomial equations with all integer roots which we compute. The eigen-abelian varieties for these endomorphisms are generalizations of Prym-Tjurin varieties and naturally contain special curves representing cohomology classes which are not expected to be represented by curves in generic abelian varieties.

math.AG↗