Characterizing $(d,h)$-elliptic stable irreducible curves

TL;DR

This paper characterizes irreducible stable curves that are limits of smooth curves admitting degree-d maps to genus-h curves, using admissible covers to understand their structure and properties.

Contribution

It introduces a new characterization of $(d,h)$-elliptic stable curves via admissible covers, extending the understanding of their degenerations.

Findings

Provides a criterion for $(d,h)$-elliptic stable curves

Connects stable curves with finite maps to smooth curves

Enhances understanding of degenerations in algebraic geometry

Abstract

We use admissible covers to characterize irreducible stable curves that are $(d,h)$-elliptic, that is, that are limits of smooth curves admiting finite maps of degree-$d$ to smooth curves of genus $h\geq 1$.