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Stable degenerations of surfaces isogenous to a product of curves

Author: Michael van Opstall
Journal: Proc. Amer. Math. Soc. 134 (2006), 2801-2806
MSC (2000): Primary 14J10
Published electronically: April 11, 2006
MathSciNet review: 2231601
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Abstract: We show that an example of Catanese yields nonrigid surfaces that are diffeomorphic, yet lie on different connected components of the moduli space of stable surfaces.

References [Enhancements On Off] (What's this?)

  • [AAL81] W. A. Adkins, A. Andreotti, and J. V. Leahy.
    Weakly normal complex spaces, volume 55 of Contributi del Centro Linceo Interdisciplinare di Scienze Matematiche e loro Applicazioni.
    Accademia Nazionale dei Lincei, Rome, 1981. MR 0695003 (84g:32013)
  • [Ale94] V. Alexeev.
    Boundedness and $ K^2$ for log surfaces.
    Internat. J. Math., 5(6):779-810, 1994. MR 1298994 (95k:14048)
  • [BC04] I. Bauer and F. Catanese.
    Some new surfaces with $ p_g=q=0$.
    The Fano Conference, 123-142.
    Univ. Torino, Turin. 2004. MR 2112572 (2005k:14079)
  • [Cat00] F. Catanese.
    Fibred surfaces, varieties isogenous to a product and related moduli spaces.
    Amer. J. Math., 122(1):1-44, 2000. MR 1737256 (2001i:14048)
  • [Cat03] F. Catanese.
    Moduli spaces of surfaces and real structures.
    Ann. of Math., 158:539-554, 2003. MR 2018929 (2005d:14053)
  • [HM98] J. Harris and I. Morrison.
    Moduli of curves, volume 187 of Graduate Texts in Mathematics.
    Springer-Verlag, New York, 1998. MR 1631825 (99g:14031)
  • [KK02] V. Kulikov and V. Kharlamov.
    On real structures on rigid surfaces.
    Izv. Math., 66(1):133-150, 2002. MR 1917540 (2003h:14089)
  • [KM98] J. Kollár and S. Mori.
    Birational geometry of algebraic varieties, volume 134 of Cambridge Tracts in Mathematics.
    Cambridge University Press, Cambridge, 1998. MR 1658959 (2000b:14018)
  • [Kol90] J. Kollár.
    Projectivity of complete moduli.
    J. Differential Geom., 32(1):235-268, 1990. MR 1064874 (92e:14008)
  • [KSB88] J. Kollár and N. I. Shepherd-Barron.
    Threefolds and deformations of surface singularities.
    Invent. Math., 91(2):299-338, 1988. MR 0922803 (88m:14022)
  • [Man01] M. Manetti.
    On the moduli space of diffeomorphic algebraic surfaces.
    Invent. Math., 143(1):29-76, 2001. MR 1802792 (2001j:14050)
  • [Tuf93] S. Tufféry.
    Déformations de courbes avec action de groupe.
    Forum Math., 5(3):243-259, 1993. MR 1216034 (94d:14012)
  • [vO05] M. A. van Opstall.
    Moduli of products of curves.
    Arch. Math. (Basel), 84(2):148-154, 2005. MR 2120708

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Additional Information

Michael van Opstall
Affiliation: Departmant of Mathematics, University of Utah, 155 South 1400 East, Room 233, Salt Lake City, Utah 84112-0090

Received by editor(s): December 16, 2004
Received by editor(s) in revised form: April 18, 2005
Published electronically: April 11, 2006
Communicated by: Michael Stillman
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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