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BGMS Seminar: Moduli of surfaces in P^3 February 21, 2019 (01:30 PM PST - 02:30 PM PST)
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Location: MSRI: Simons Auditorium
Speaker(s) Kristin DeVleming (University of California, San Diego)
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We will discuss a stable pair compactification of the moduli space of degree d surfaces in P^3.  These compactifications, introduced by Koll\'ar and Shepherd-Barron arising from ideas in the Minimal Model Program, are generally difficult to describe explicitly.  Motivated by work of Hacking, who obtained an explicit modular compactification for plane curves, we consider a surface S in P^3 as a pair (P^3, S).  Then, using a particular enlarged class of these pairs, we can compactify the moduli space of such surfaces.  Using this framework, for surfaces of odd degree d, we obtain a rough classification of the singular objects on the boundary of this moduli space and will discuss some divisorial components of the boundary.  We give a more detailed description for quintic surfaces. 

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