Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The geometric genus of a desingularized fiber product of elliptic surfaces


Author: Chad Schoen
Journal: Proc. Amer. Math. Soc. 141 (2013), 745-752
MSC (2010): Primary 14J30, 14D99, 14E99
DOI: https://doi.org/10.1090/S0002-9939-2012-11426-1
Published electronically: July 3, 2012
MathSciNet review: 3003668
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A formula for the geometric genus is given under the assumption of tame ramification.


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

  • 1. Barth, W.; Peters, C.; Van de Ven, A. Compact complex surfaces. Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 4. Springer-Verlag, Berlin, 1984. MR 749574 (86c:32026)
  • 2. Chatzistamatiou, A.; Rülling, K., Higher direct images of the structure sheaf in positive characteristic, to appear in Algebra and Number Theory.
  • 3. Cossart, V.; Piltant, O., Resolution of singularities of threefolds in positive characteristic. II. J. Algebra 321 (2009), no. 7, 1836-1976. MR 2494751 (2010c:14009)
  • 4. Cutkosky, S., Resolution of singularities for 3-folds in positive characteristic. Amer. J. Math 131 (2009), no. 1, 59-127. MR 2488485 (2010e:14010)
  • 5. Donagi, R.; Ovrut, B.; Pantev, T.; Waldram, D., Standard-model bundles. Adv. Theor. Math. Phys. 5 (2001), no. 3, 563-615. MR 1898371 (2003i:14012)
  • 6. Drinfeld, V., Elliptic modules, Math. USSR Sbornik 23 (1974), 561-592. MR 0384707 (52:5580)
  • 7. Ellingsrud, G.; Lønsted, K., An equivariant Lefschetz formula for finite reductive groups, Math. Ann. 251 (1980), 253-261. MR 589254 (81k:14039)
  • 8. Grothendieck, A., Sur quelques points d'algèbre homologique. Tôhoku Math. J. (2) 9 (1957), 119-121. MR 0102537 (21:1328)
  • 9. Hartshorne, R., Algebraic Geometry, Graduate Texts in Math. 52, Springer, New York, 1977. MR 0463157 (57:3116)
  • 10. Kollár, J., Lectures on Resolution of Singularities, Annals of Math. Studies 166, Princeton University Press, Princeton and Oxford, 2007. MR 2289519 (2008f:14026)
  • 11. Liu, Q., Algebraic Geometry and Arithmetic Curves, Oxford Graduate Texts in Mathematics 6, Oxford University Press, Oxford, 2002. MR 1917232 (2003g:14001)
  • 12. Meyer, C., Modular Calabi-Yau Threefolds, Fields Institute Monograph 22, American Mathematical Society, Providence, RI, 2005. MR 2176545 (2007f:11070)
  • 13. Milne, J., Étale Cohomology, Princeton University Press, 1980. MR 559531 (81j:14002)
  • 14. Neukirch, J., Algebraic Number Theory, Grundlehren der Mathematischen Wissenschaften 322, Springer, 1999. MR 1697859 (2000m:11104)
  • 15. Saito, T., Vanishing cycles and geometry of curves over a discrete valuation ring. Amer. J. Math. 109 (1987), no. 6, 1043-1085. MR 919003 (88h:14036)
  • 16. Schoen, C., Desingularized fiber products of semi-stable elliptic surfaces with vanishing third Betti number. Compos. Math. 145 (2009), no. 1, 89-111. MR 2480496 (2010b:14077)
  • 17. Schoen, C.; Top, J., Drinfeld modules and torsion in the Chow groups of certain threefolds. Proc. Lond. Math. Soc. (3) 95 (2007), no. 3, 545-566. MR 2368276 (2008m:14020)
  • 18. Silverman, J., The Arithmetic of Elliptic Curves, Graduate Texts in Math. 106, Springer, 1986. MR 817210 (87g:11070)
  • 19. Silverman, J., Advanced Topics in the Arithmetic of Elliptic Curves, Graduate Texts in Math. 151, Springer, New York, 1994. MR 1312368 (96b:11074)
  • 20. Viehweg, E., Rational singularities of higher dimensional schemes. Proc. A.M.S. 63 (1977), 6-8. MR 0432637 (55:5624)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 14J30, 14D99, 14E99

Retrieve articles in all journals with MSC (2010): 14J30, 14D99, 14E99


Additional Information

Chad Schoen
Affiliation: Department of Mathematics, Physics Building, Duke University, Research Drive, Durham, North Carolina 27708-0320

DOI: https://doi.org/10.1090/S0002-9939-2012-11426-1
Received by editor(s): January 30, 2011
Received by editor(s) in revised form: July 10, 2011
Published electronically: July 3, 2012
Communicated by: Lev Borisov
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society