Families of elliptic curves in $\mathbb{P}^3$ and Bridgeland Stability

Michigan Math. J. 67 (2018), no. 4, 787-813 We study wall crossings in Bridgeland stability for the Hilbert scheme of elliptic quartic curves in three dimensional projective space. We provide a geometric description of each of the moduli spaces we encounter, including when the second component of th...

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Bibliographic Details
Main Authors Gallardo, Patricio, Huerta, César Lozano, Schmidt, Benjamin
Format Journal Article
LanguageEnglish
Published 26.09.2016
Subjects
Mathematics - Algebraic Geometry
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Summary:Michigan Math. J. 67 (2018), no. 4, 787-813 We study wall crossings in Bridgeland stability for the Hilbert scheme of elliptic quartic curves in three dimensional projective space. We provide a geometric description of each of the moduli spaces we encounter, including when the second component of this Hilbert scheme appears. Along the way, we prove that the principal component of this Hilbert scheme is a double blow up with smooth centers of a Grassmannian, exhibiting a completely different proof of this known result by Avritzer and Vainsencher. This description allows us to compute the cone of effective divisors of this component.
DOI:10.48550/arxiv.1609.08184