Let (X, Delta) be a projective klt pair of dimension 2 and let L be a nef Cartier divisor on X such that K-X + Delta + L is nef. As a complement to the Generalized Abundance Conjecture by Lazic and Peternell, we prove that if K-X + Delta and L are not proportional modulo numerical equivalence, then K-X + Delta + L is semiample. An example due to Lazic shows that this is no longer true in any dimension n >= 3.
A remark on generalized abundance for surfaces / Fontanari, Claudio. - In: EUROPEAN JOURNAL OF MATHEMATICS. - ISSN 2199-675X. - 10:1(2024), pp. 71-74. [10.1007/s40879-023-00716-y]
A remark on generalized abundance for surfaces
Fontanari, Claudio
2024-01-01
Abstract
Let (X, Delta) be a projective klt pair of dimension 2 and let L be a nef Cartier divisor on X such that K-X + Delta + L is nef. As a complement to the Generalized Abundance Conjecture by Lazic and Peternell, we prove that if K-X + Delta and L are not proportional modulo numerical equivalence, then K-X + Delta + L is semiample. An example due to Lazic shows that this is no longer true in any dimension n >= 3.File in questo prodotto:
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