Nef divisors on M_0,n from GIT

2008/12/03 by Valery Alexeev, Alexeev, Valery, David Swinarski +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.0812.0778

openalex publication_date 2008/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce and study the GIT CONE of M_0,n, which is generated by the pullbacks of the natural ample line bundles on the GIT quotients (\mathbb P¹)ⁿ//SL(2). We give an explicit formula for these line bundles and prove a number of basic results about the GIT cone. As one application, we prove unconditionally that the log canonical models of M_0,n with a symmetric boundary divisor coincide with the moduli spaces of weighted curves or with the symmetric GIT quotient, extending the result of Matt Simpson arXiv:0709.4037. (Cf. also a different proof by Fedorchuk and Smyth arXiv:0810.1677)

Citations

• On Log Canonical Models of the Moduli Space of Stable Pointed Curves

Cited by

• Moduli spaces of weighted pointed stable rational curves via GIT
• sl₂ conformal block divisors and the nef cone of M_0,n

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