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Moduli of weighted stable marked del Pezzo surfaces

Author:
Nolan Schock
Keyword:
Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG)
journal:
--
date:
2023-05-10 16:00:00
Abstract
For $n \leq 6$, we describe the stable pair compactification $\overline{Y}_c^n$ of the moduli space $Y_c^n$ of log canonical pairs $(S,cB)$ such that $S$ is a smooth del Pezzo surface of degree $9-n$, $B$ is the (labeled) sum of its finitely many lines, and $c \in (0,1]$ such that $K_S+cB$ is ample. When $c=1$ or $c$ is minimal, this compactification has been described previously by work of Hacking-Keel-Tevelev, and Gallardo-Kerr-Schaffler. We establish the full sequence of wall crossings as one decreases $c$ from 1 to the minimal weight. Our results include a complete description of the fibers of the universal families.
PDF: Moduli of weighted stable marked del Pezzo surfaces.pdf
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