Families of elliptic curves and Bridgeland stability (César Lozano)

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Families of elliptic curves and Bridgeland stability

Plática dada por César Lozano (Catedra CONACyT) en el Segundo Congreso Nacional de Geometría Algebraica el miércoles 28 de febrero del 2018 Casa Matemática Oaxaca, en Oaxaca de Juárez, México

Abstract:
In algebraic geometry, we often want to understand algebraic varieties in families instead of in isolation. Hilbert schemes are spaces whose geometry tells us almost everything about families of embedded algebraic varieties. However, in general, the geometry of these schemes is often very hard to understand, so each example may help build our intuition and shape future results.

In this talk, I will present an explicit description of the geometry of the Hilbert scheme of elliptic curves in projective 3-space making use of Bridgeland stability conditions. In doing so, we observe the following, which I’ll make precise in the talk: wall-crossing corresponds to running the Minimal Model Program.

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César Lozano:
http://www.matem.unam.mx/fsd/lozano

Articulos de Manuel González Villa
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