Continuous Linear Series

2025/10/13 by Esteves, Eduardo, Nigro, Antonio, Rizzo, Pedro
#14C05 #14D22 #14H10 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.11623

Abstract

We parameterize by a fine moduli space all degenerations of linear series to a singular curve which is the union of two smooth components meeting transversally at a single point. For this we introduce a novel object in the study of degenerations of linear series, which is the continuous linear series. Our moduli space can be regarded as a Hilbert quotient, in the terminology introduced by Kapranov, and is a new compactification of Osserman moduli space of exact limit linear series, and consequently, of Eisenbud and Harris moduli space of refined limit linear series on the curve.

Citations

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Related

• Moduli of Crude Limit Linear Series
• Level-δ limit linear series
• Linear series with ρ< 0 via thrifty lego-building
• Moduli spaces of curves with linear series and the slope conjecture
• Limit linear series for curves not of compact type