Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
  Journal of Algebraic Geometry
Journal of Algebraic Geometry
  
Online ISSN 1534-7486; Print ISSN 1056-3911
 

Effective divisors on $\overline{\mathcal{M}}_g$, curves on $K3$ surfaces, and the slope conjecture


Authors: Gavril Farkas and Mihnea Popa
Journal: J. Algebraic Geom. 14 (2005), 241-267
Published electronically: November 18, 2004
MathSciNet review: 2123229
Full-text PDF

Abstract | References | Additional Information

Abstract: We compute the class of the compactification of the divisor of curves sitting on a $K3$ surface and show that it violates the Harris-Morrison Slope Conjecture. We carry this out using the fact that this divisor has four distinct incarnations as a geometric subvariety of the moduli space of curves. We also give a counterexample to a hypothesis raised by Harris and Morrison that the Brill-Noether divisors are essentially the only effective divisors on the moduli space of curves having minimal slope $6+12/(g+1)$.


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


Additional Information

Gavril Farkas
Affiliation: Department of Mathematics, Princeton University, Fine Hall, Princeton, New Jersey 08544
Address at time of publication: Department of Mathematics, University of Texas at Austin, 1 University Station C1200, Austin, Texas 78712
Email: gfarkas@math.princeton.edu

Mihnea Popa
Affiliation: Department of Mathematics, Harvard University, One Oxford Street, Cambridge, Massachusetts 02138
Email: mpopa@math.harvard.edu

DOI: http://dx.doi.org/10.1090/S1056-3911-04-00392-3
PII: S 1056-3911(04)00392-3
Received by editor(s): May 16, 2003
Published electronically: November 18, 2004
Additional Notes: The first author’s research was partially supported by NSF Grant DMS-0140520. The second author’s research was partially supported by NSF Grant DMS-0200150


Journal of Algebraic Geometry
The Journal of Algebraic Geometry
is sponsored by the Department of Mathematical Sciences
of Tsinghua University
and is distributed by the American Mathematical Society
for University Press, Inc.
Online ISSN 1534-7486; Print ISSN 1056-3911
© 2014 University Press, Inc.
Comments: jag-query@ams.org
AMS Website