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比利时vs摩洛哥足彩 ,
university of california san diego

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math 208 - seminar in algebraic geometry

kristin devleming

ucsd

moduli of surfaces in $\mathbb{p}^3$

abstract:

for fixed degree $d$, one could ask for a meaningful compactification of the moduli space of smooth degree $d$ surfaces in $\mathbb{p}^3$. in other words, one could ask for a parameter space whose interior points correspond to [isomorphism classes of] smooth surfaces and whose boundary points correspond to degenerations of these surfaces. motivated by hacking's work for plane curves, i will discuss a ksba compactification of this space by considering a surface $s$ in $\mathbb{p}^3$ as a pair $(\mathbb{p}^3, s)$ satisfying certain properties. we will study an enlarged class of these pairs, including singular degenerations of both $s$ and the ambient space. the moduli space of the enlarged class of pairs will be the desired compactification and, as long as the degree $d$ is odd, we can give a rough classification of the objects on the boundary of the moduli space.

october 5, 2018

2:00 pm

ap&m 5829

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