2020/09/13 by Nolan Schock, Schock, Nolan
Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #math.AG
paper · pdf · doi:10.48550/arxiv.2009.06056
34 pages, 1 figure
arxiv created 2020/09/13 · openalex publication_date 2020/09/13 · arxiv updated 2020/09/15 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We describe sequences of blowups of M0,5 × M0,5 and P2 × P2 yielding a small resolution of the stable pair compactification M(3,6) of the moduli space M(3,6) of six lines in P2. These blowup sequences can be viewed, respectively, as generalizations of Keel's and Kapranov's constructions of M0,n. We use these blowup sequences to describe the intersection theory of M(3,6). In particular, we show that the Chow ring of any small resolution of M(3,6) has a presentation analogous to Keel's presentation of A^*(M0,n), and the Chow ring of M(3,6) is an explicit subring of the Chow ring of one of these small resolutions. We also introduce higher-dimensional versions of the ψ-classes on M0,n, and describe their intersections on M(3,6). Finally, we use our results to obtain an independent proof of Luxton's result that M(3,6) is the log canonical compactification of M(3,6).