Linear series on a curve of compact type bridged by a chain of elliptic curves

TL;DR

This paper studies the existence of limit linear series on certain reducible curves, revealing how Brill-Noether loci of low codimension have distinct supports, thereby advancing understanding of linear series on complex curves.

Contribution

It provides new non-existence conditions for limit linear series on curves of compact type bridged by elliptic chains, linking these to Brill-Noether loci properties.

Findings

Non-existence conditions for certain limit linear series.

Distinct supports of Brill-Noether loci of codimension two.

Relations among Brill-Noether loci in the moduli space.

Abstract

In the present paper we investigate conditions for the non-existence of a limit linear series on a curve of compact type such that two smooth curves are bridged by a chain of two elliptic curves. Combining this work with results on the existence of a smoothable limit linear series on such a curve, we show relations among Brill-Noether loci of codimension at most two in the moduli space of complex curves. Specifically, Brill-Noether loci of codimension two have mutually distinct supports.