Moduli of surfaces in ${{\mathbb {P}}}^{3}$

Compositio mathematica

article

Kristin DeVleming¹ 

[1] Department of Mathematics, University of Massachusetts

关键词: algebraic geometry;    birational geometry and moduli spaces;    moduli of stable pairs;    14J10;    14J29;    14J70;    14E30;   

DOI  :  10.1112/S0010437X22007552

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

The main goal of this paper is to construct a compactification of the moduli space of degree $d \geqslant 5$ surfaces in $\mathbb {P}^{3}_{{{\mathbb {C}}}}$ , 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 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.

【 授权许可】

CC BY