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 Mosc. Math. J., 2004, Volume 4, Number 1, Pages 181–198 (Mi mmj147)

Moduli stacks $\overline L_{g,S}$

Yu. I. Maninab

a Max Planck Institute for Mathematics
b Northwestern University

Abstract: This paper is a sequel to the paper by A. Losev and Yu. Manin, in which new moduli stacks $\overline L_{g,S}$ 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 another paper by Losev and Manin. In this paper the basic geometric properties of $\overline L_{g,S}$ 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 $H^*(\overline M_{0,S})$.

Key words and phrases: Stable pointed curves, moduli spaces, generalized Keel's relations.

DOI: https://doi.org/10.17323/1609-4514-2004-4-1-181-198

Full text: http://www.ams.org/.../abst4-1-2004.html
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Bibliographic databases:

MSC: Primary 14N35; Secondary 14H10, 53D45
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Citation: Yu. I. Manin, “Moduli stacks $\overline L_{g,S}$”, Mosc. Math. J., 4:1 (2004), 181–198

Citation in format AMSBIB
\Bibitem{Man04} \by Yu.~I.~Manin \paper Moduli stacks $\overline L_{g,S}$ \jour Mosc. Math.~J. \yr 2004 \vol 4 \issue 1 \pages 181--198 \mathnet{http://mi.mathnet.ru/mmj147} \crossref{https://doi.org/10.17323/1609-4514-2004-4-1-181-198} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2074988} \zmath{https://zbmath.org/?q=an:1082.14057} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000208594500008} 

• http://mi.mathnet.ru/eng/mmj147
• http://mi.mathnet.ru/eng/mmj/v4/i1/p181

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Arend Bayer, Yu. I. Manin, “Stability conditions, wall-crossing and weighted Gromov–Witten invariants”, Mosc. Math. J., 9:1 (2009), 3–32
2. Ceyhan Ö., “Chow groups of the moduli spaces of weighted pointed stable curves of genus zero”, Adv. Math., 221:6 (2009), 1964–1978
3. Birkar C., Cascini P., Hacon Ch.D., McKernan J., “Existence of minimal models for varieties of log general type”, J. Amer. Math. Soc., 23:2 (2010), 405–468