Effective divisors on M̄g, curves on K3 surfaces, and the slope conjecture

Gavril Farkas*, Mihnea Popa

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

43 Scopus citations

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).

Original languageEnglish (US)
Pages (from-to)241-267
Number of pages27
JournalJournal of Algebraic Geometry
Volume14
Issue number2
DOIs
StatePublished - Apr 2005

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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