# On the cone of effective 2-cycles on $\overline{M}_{0,7}$.

##
Luca Shaffler

created by risa on 29 May 2015

4 jun 2015
-- 14:30

Aula 211, Dip. Matematica, Università "Roma Tre", Roma

**Abstract.**

Fulton's question about effective k-cycles on $\overline{M}_{0,n}$ for
1<k<n-4 can be answered negatively by appropriately lifting to
$\overline{M}_{0,n}$ the Keel-Vermeire divisors on
$\overline{M}_{0,k+1}$. In this talk we focus on the case of 2-cycles
on $\overline{M}_{0,7}$, and we prove that the 2-dimensional boundary
strata together with the lifts of the Keel-Vermeire divisors are not
enough to generate the cone of effective 2-cycles. We do this by
providing examples of effective 2-cycles on $\overline{M}_{0,7}$ that
cannot be written as an effective combination of the aforementioned
2-cycles. These examples are inspired by a blow up construction of
Castravet and Tevelev.