## The Michigan Mathematical Journal

### Families of Elliptic Curves in $\mathbb{P}^{3}$ and Bridgeland Stability

#### Abstract

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

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

Dates
Revised: 14 September 2017
First available in Project Euclid: 5 October 2018

https://projecteuclid.org/euclid.mmj/1538705132

Digital Object Identifier
doi:10.1307/mmj/1538705132

Mathematical Reviews number (MathSciNet)
MR3877437

Zentralblatt MATH identifier
07056369

#### Citation

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. https://projecteuclid.org/euclid.mmj/1538705132

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