Harvard-MIT Algebraic Geometry Seminar

A new candidate for the nef cone of $\overline{M}_{g,n}$ Click here for pdf

Angela Gibney U Penn

There is a well known upper bound $F_{g,n}$ for the nef coneNef$(\overline{M}_{g,n})$ of $\overline{M}_{g,n}$.  The cone $F_{g,n}$ is an explicitly defined, polyhedral cone that contains Nef$(\overline{M}_{g,n})$.  The F-conjecture asserts that Nef$(\overline{M}_{g,n})=F_{g,n}$ and is known to be true for example, when $g=0$ and $n \le 7$, and when $n=0$, $g \le 24$ as well as for a number of cases in between. In this talk, I will describe a new candidate for the nef cone of $\overline{M}_{g,n}$.  This is a polyhedral cone $C_{g,n}$ that D. Maclagan and I have proved is a sub cone of $F_{g,n}$.  We can show that if $F_{g,n}$ were also contained in $C_{g,n}$, then it would imply that Nef$(\overline{M}_{g,n})=F_{g,n}=C_{g,n}$. In the special case $g=0$, we can show that $C_{0,n}$ is a sub cone of Nef$(\overline{M}_{0,n})$ and for low $n$, all three cones are equal.

Tuesday October 9th 3:00 p.m. MIT (2-142)