The Michigan Mathematical Journal

Families of Elliptic Curves in P3 and Bridgeland Stability

Patricio Gallardo, César Lozano Huerta, and Benjamin Schmidt

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We study wall crossings in Bridgeland stability for the Hilbert scheme of elliptic quartic curves in the 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 blowup 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.

Article information

Michigan Math. J., Volume 67, Issue 4 (2018), 787-813.

Received: 22 December 2016
Revised: 14 September 2017
First available in Project Euclid: 5 October 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14H10: Families, moduli (algebraic)
Secondary: 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20] 18E30: Derived categories, triangulated categories


Gallardo, Patricio; Lozano Huerta, César; Schmidt, Benjamin. Families of Elliptic Curves in $\mathbb{P}^{3}$ and Bridgeland Stability. Michigan Math. J. 67 (2018), no. 4, 787--813. doi:10.1307/mmj/1538705132.

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