Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
home | mail | papers | authors | news | seminars | events | open positions | login

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


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.

Credits | Cookie policy | HTML 5 | CSS 2.1