Moduli of Crude Limit Linear Series

Abstract

Eisenbud and Harris introduced the theory of limit linear series and constructed a space parameterizing their limit linear series. Recently, Osserman introduced a new space which compactifies the Eisenbud-Harris construction. In the Eisenbud-Harris space, the set of refined limit linear series is always dense on a general reducible curve. Osserman asks when the same is true for his space. In this paper, we answer his question by characterizing the situations when the crude limit linear series contain a nonempty open subset of his space. We also show that the exact points are always dense.