# Mathematical Sciences Research Institute

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# Seminar

Basic Notions Seminar: The Slope "Conjecture'' May 07, 2009
Location: MSRI: Simons Auditorium
Speaker(s) Ian Morrison
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Abstract/Media

The talk will give an introductory survey of results about effective divisors on moduli spaces of stable curves. The main focus will be on the special case of $\overline{M_g}$ when there has been considerable work on finding $s_g$, defined as the smallest slope $s$ such that the ray $s \lambda- \delta$ contains effective classes. I will review the history of the problem and the conjectural lower bound of the title, then discuss counterexamples to it due mainly to Farkas, and recent lower bounds due to Chen, Fedorchuk, Pandharipande and others. Time permitting, I will also discuss a few results for other moduli spaces of stable curves.