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 language | English (US) |
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Pages (from-to) | 241-267 |
Number of pages | 27 |
Journal | Journal of Algebraic Geometry |
Volume | 14 |
Issue number | 2 |
DOIs | |
State | Published - Apr 2005 |
ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology