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Summary: WEIGHTED GRASSMANNIANS AND STABLE HYPERPLANE
ARRANGEMENTS
VALERY ALEXEEV
Abstract. We give a common generalization of (1) Hassett's weighted stable
curves, and (2) Hacking-Keel-Tevelev's stable hyperplane arrangements.
Contents
1. Introduction and main statements 1
2. Matroid polytopes 4
3. Moduli spaces for varieties with torus action 7
4. Review of the unweighted case 8
5. Weighted grassmannians 9
6. GIT theory of the universal family over the grassmanian 10
7. Definitions of the moduli space and the family 13
8. Completing the proofs of main theorems 16
9. Some simple examples 17
References 19
1. Introduction and main statements
The moduli space M0,n of stable n-pointed rational curves has many generaliza-
tions, beginning of course with Mg,n. For this paper, however, the following two
generalizations will be important:
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