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Notes on the Construction of the Moduli Space of Curves

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Recent Progress in Intersection Theory

Part of the book series: Trends in Mathematics ((TM))

Abstract

The purpose of these notes is to discuss the problem of moduli for curves of genus g ≥ 31 and outline the construction of the (coarse) moduli scheme of stable curves due to Gieseker. The notes are broken into four parts.

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References

  1. M. Artin, G. Winters, Degenerate fibres and stable reduction of curves, Topology 10 (1971), 373–383

    Article  MathSciNet  MATH  Google Scholar 

  2. P. Deligne, D. Mumford, Irreducibility of the space of curves of given genus, Publ. Math. IHES 36 (1969), 75–110

    MathSciNet  MATH  Google Scholar 

  3. S. Diaz, A bound on the dimensions of complete subvarieties of M g Duke Math. J. 51 (1984), 405–408

    Article  MATH  Google Scholar 

  4. I. Dolgachev, Rationality of fields of invariants, in Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine,1985), Proc. Sympos. Pure Math. 46 Part 2, 3–15 (1987)

    MathSciNet  Google Scholar 

  5. A. Grothendieck, Etudes locales des schémas et des morphismes des schemas, Publ. Math. IHES, 32 (1967)

    Google Scholar 

  6. W. Fulton, Hurwitz schemes and irreducibility of moduli of of algebraic curves, Ann. Math. 90 (1969), 542–575

    Article  MathSciNet  MATH  Google Scholar 

  7. W. Fulton, On the irreducibility of the moduli space of curves, appendix to a paper of Harris and Mumford, Invent. Math. 67 (1982), 87–88

    Article  MathSciNet  MATH  Google Scholar 

  8. D. Gieseker, Tata lectures on moduli of curves, Springer-Verlag, NY, (1982)

    Google Scholar 

  9. H. Gillet, Intersection theory on algebraic stacks and Q-varieties, J. Pure Appl. Alg. 34 (1984), 193–240

    Article  MathSciNet  MATH  Google Scholar 

  10. J. Harris, D. Mumford, On the Kodaira dimension of the moduli space of curves, Invent. Math. 67 23–86 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  11. S. Keel, S. Mori, Quotients by groupoids, Ann. Math. 145 (1997), 193–213

    Article  MathSciNet  MATH  Google Scholar 

  12. G. Laumon, L. Moret-Bailly, Champs algébriques, preprint

    Google Scholar 

  13. D. Mumford, J. Fogarty, F. Kirwan, Geometric Invariant Theory, Third Enlarged Edition, Springer-Verlag, NY, (1994)

    Book  Google Scholar 

  14. A. Vistoli, Intersection theory on algebraic stacks and their moduli spaces, Invent. Math. 97 (1989), 613–670

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Missouri, Columbia, MO, 65211, USA

    Dan Edidin

Authors
  1. Dan Edidin
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Oslo, N-0316, Oslo, Sweden

    Geir Ellingsrud

  2. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA

    William Fulton

  3. Departimento di Matematica, Università di Bologna, Bologna, 40127, Italy

    Angelo Vistoli

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© 2000 Springer Science+Business Media New York

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Edidin, D. (2000). Notes on the Construction of the Moduli Space of Curves. In: Ellingsrud, G., Fulton, W., Vistoli, A. (eds) Recent Progress in Intersection Theory. Trends in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1316-1_3

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  • DOI: https://doi.org/10.1007/978-1-4612-1316-1_3

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7090-4

  • Online ISBN: 978-1-4612-1316-1

  • eBook Packages: Springer Book Archive

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