Linear series on a stable curve of compact type and relations among Brill-Noether loci

Abstract

Let C be a stable curve of compact type such that two smooth curves with general moduli are bridged by a chain of n-elliptic curves, which will be called a TCBE curve. In the present paper, we investigate the existence of a smoothable limit linear series on C whose Brill-Noether number ρ satisfies −n≤ρ<0. Through this work, we find some relationships between a family of TCBE curves of genus g and a Brill-Noether locus in the moduli space of stable curves of genus g. Further, these results show some relations among Brill-Noether loci.