Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format 		Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

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
Posted: April 11, 2006
MathSciNet review: 2231601
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

  • [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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 14J10

Retrieve articles in all journals with MSC (2000): 14J10

Additional Information

Michael van Opstall
Affiliation: Departmant of Mathematics, University of Utah, 155 South 1400 East, Room 233, Salt Lake City, Utah 84112-0090
Email: opstall@math.utah.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08517-0
PII: S 0002-9939(06)08517-0
Received by editor(s): December 16, 2004
Received by editor(s) in revised form: April 18, 2005
Posted: April 11, 2006
Communicated by: Michael Stillman
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia