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تسجيل مستخدم جديدModuli of surfaces in $mathbb{P}^3$
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تأليف
Kristin DeVleming
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The goal of this paper is to construct a compactification of the moduli space of degree $d ge 5$ surfaces in $mathbb{P}^3$, i.e. a parameter space whose interior points correspond to (equivalence classes of) smooth surfaces in $mathbb{P}^3$ and whose boundary points correspond to degenerations of such surfaces. We study a more general problem and consider a divisor $D$ on a Fano variety $Z$ as a pair $(Z, D)$ satisfying certain properties. We find a modular compactification of such pairs and, in the case of $Z = mathbb{P}^3$ and $D$ a surface, use their properties to classify the pairs on the boundary of the moduli space.
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