Fulton's question about effective k-cycles on (M) over bar (0),(n) for 1 < k < n - 4 can be answered negatively by appropriately lifting to (M) over bar (0),(n) the Keel-Vermeire divisors on (M) over bar (0), (k+1). In this paper we focus on the case of 2-cycles on (M) over bar (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) over bar (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.

Schaffler, L. (2015). On the cone of effective 2-cycles on $\overline{M}_{0,7}$. EUROPEAN JOURNAL OF MATHEMATICS, 1(4), 669-694 [10.1007/s40879-015-0072-2].

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

Luca Schaffler
2015-01-01

Abstract

Fulton's question about effective k-cycles on (M) over bar (0),(n) for 1 < k < n - 4 can be answered negatively by appropriately lifting to (M) over bar (0),(n) the Keel-Vermeire divisors on (M) over bar (0), (k+1). In this paper we focus on the case of 2-cycles on (M) over bar (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) over bar (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.
Schaffler, L. (2015). On the cone of effective 2-cycles on $\overline{M}_{0,7}$. EUROPEAN JOURNAL OF MATHEMATICS, 1(4), 669-694 [10.1007/s40879-015-0072-2].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/423927
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