Pseudoeffective and nef classes on abelian varieties
By O. Debarre, L. Ein, R. Lazarsfeld, Claire Voisin. Compositio Mathematica, 2010
80 citations recorded by the source corpus.
Abstract We study the cones of pseudoeffective and nef cycles of higher codimension on the self product of an elliptic curve with complex multiplication, and on the product of a very general abelian surface with itself. In both cases, we find for instance the existence of nef classes that are not pseudoeffective, answering in the negative a question raised by Grothendieck in correspondence with Mumford. We also discuss several problems and questions for further investigation.
View Paper: https://www.semanticscholar.org/paper/89657253831db343575c223e299706d82249bf91
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Citations in the corpus
- Degrees of iterates of rational maps on normal projective varieties (2017, background): “For cycles of intermediate dimension this situation is, however, more subtle and was only recently seriously considered (see [3, 4, 8] and the recent series of papers by Fulger and Lehmann [14, 15].”