Moduli stacks $\bar{L}_{g,S}$

Details Moduli stacks $\bar{L}_{g,S}$ Moduli stacks $\bar{L}_{g,S}$

2002-06-12

arxiv.org/abs/math/0206123v2

Mathematics

Algebraic Geometry

20 pp., amstex file, no figures

Scientific paper

This paper is a sequel to the paper by A. Losev and Yu. Manin [LoMa1], in which new moduli stacks $\bar{L}_{g,S}$ of pointed curves were introduced. They classify curves endowed with a family of smooth points divided into two groups, such that the points of the second group are allowed to coincide. The homology of these stacks form components of the extended modular operad whose combinatorial models are further studied in [LoMa2]. In this paper the basic geometric properties of $\bar{L}_{g,S}$ are established using the notion of weighted stable pointed curves introduced recently by B. Hassett. The main result is a generalization of Keel's and Kontsevich -- Manin's theorems on the structure of $H^*(\bar{M}_{0,S}).$

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