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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