Skip to main content

Singular Curves

  • 1028 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 2122)

Abstract

The aim of this chapter is to collect the definitions and basic properties of the curves that we will deal with throughout the manuscript.

Keywords

  • Singular Curves
  • Manuscript
  • Subcurve
  • Elliptic Tails
  • Bubble Node

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   49.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions
Fig. 2.1

References

  1. J. Alper, Adequate moduli spaces and geometrically reductive group schemes. Algebr. Geom. Preprint available at arXiv:1005.2398 (to appear)

    Google Scholar 

  2. J. Alper, D.I. Smyth, F. van der Wyck, Weakly proper moduli stacks of curves. Preprint available at arXiv:1012.0538

    Google Scholar 

  3. E. Arbarello, M. Cornalba, P.A. Griffiths, Geometry of Algebraic Curves. Volume II. With a contribution by Joseph Daniel Harris. Grundlehren der Mathematischen Wissenschaften, vol. 268 (Springer, Heidelberg, 2011)

    Google Scholar 

  4. L. Caporaso, A compactification of the universal Picard variety over the moduli space of stable curves. J. Am. Math. Soc. 7, 589–660 (1994)

    CrossRef  MATH  MathSciNet  Google Scholar 

  5. F. Catanese, Pluricanonical-Gorenstein-curves, in Enumerative Geometry and Classical Algebraic Geometry (Nice, 1981). Progress in Mathematics, vol. 24 (Birkhäuser Boston, Boston, 1982), pp. 51–95

    Google Scholar 

  6. P. Deligne, D. Mumford, The irreducibility of the space of curves of given genus. Inst. Hautes Études Sci. Publ. Math. 36, 75–109 (1969)

    CrossRef  MATH  MathSciNet  Google Scholar 

  7. D. Edidin, Notes on the construction of the moduli space of curves, in Recent Progress in Intersection Theory (Bologna, 1997). Trends in Mathematics (Birkh auser Boston, Boston, 2000), pp. 85–113

    Google Scholar 

  8. D. Gieseker, Lectures on Moduli of Curves. Tata Institute of Fundamental Research Lectures on Mathematics and Physics, vol. 69 (Tata Institute of Fundamental Research, Bombay, 1982)

    Google Scholar 

  9. J. Hall, Moduli of singular curves. Preprint (2010). Available at arXiv:1011.6007v1

    Google Scholar 

  10. B. Hassett, D. Hyeon, Log canonical models for the moduli space of curves: first divisorial contraction. Trans. Am. Math. Soc. 361, 4471–4489 (2009)

    CrossRef  MATH  MathSciNet  Google Scholar 

  11. D. Hyeon, Y. Lee, Stability of tri-canonical curves of genus two. Math. Ann. 337, 479–488 (2007)

    CrossRef  MATH  MathSciNet  Google Scholar 

  12. D. Hyeon, I. Morrison, Stability of tails and 4-canonical models. Math. Res. Lett. 17(4), 721–729 (2010)

    CrossRef  MATH  MathSciNet  Google Scholar 

  13. F.F. Knudsen, The projectivity of the moduli space of stable curves. II. The stacks M g, n . Math. Scand. 52(2), 161–199 (1983)

    Google Scholar 

  14. M. Melo, Compactified Picard stacks over the moduli stack of stable curves with marked points. Adv. Math. 226, 727–763 (2011)

    CrossRef  MATH  MathSciNet  Google Scholar 

  15. D. Mumford, Stability of projective varieties. Enseignement Math. (2) 23, 39–110 (1977)

    Google Scholar 

  16. D. Schubert, A new compactification of the moduli space of curves. Compositio Math. 78, 297–313 (1991)

    MATH  MathSciNet  Google Scholar 

  17. E. Sernesi, Deformations of Algebraic Schemes. Grundlehren der mathematischen Wissenschaften, vol. 334 (Springer, New York, 2006)

    Google Scholar 

  18. D.I. Smyth, Towards a classification of modular compactifications of M g, n . Invent. Math. 192, 459–503 (2013)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Bini, G., Felici, F., Melo, M., Viviani, F. (2014). Singular Curves. In: Geometric Invariant Theory for Polarized Curves. Lecture Notes in Mathematics, vol 2122. Springer, Cham. https://doi.org/10.1007/978-3-319-11337-1_2

Download citation