Algebraic cycles from a computational point of view

Authors:
Carlos Simpson
Affiliations:
CNRS, Laboratoire J. A. Dieudonné UMR 6621, Université de Nice-Sophia Antipolis, 06108 Nice, France
Venue:
Theoretical Computer Science
Year:
2008

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Abstract

The Hodge conjecture implies decidability of the question whether a given topological cycle on a smooth projective variety over the field of algebraic complex numbers can be represented by an algebraic cycle. We discuss some details concerning this observation, and then propose that it suggests going on to actually implement an algorithmic search for algebraic representatives of classes which are known to be Hodge classes.