| Fulton's question about effective k-cycles on M 0,n can be answered negatively by appropriately lifting to M 0,n the Keel-Vermeire divisors on M 0,k+1. In this talk we focus on the case of 2-cycles on 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 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. |