Wayne State University
Mathematics Department Colloquium
Burt Totaro
University of Chicago
April 6, 1998
A survey of the Hodge conjecture
The Hodge conjecture is often considered the hardest problem
in algebraic geometry. The conjecture is an attempt to determine which
homology classes on a complex algebraic variety can be represented
by algebraic subvarieties. There are almost no general results in
this direction. I will describe some examples where the conjecture can
be checked, and some topological ideas which Atiyah and Hirzebruch
used to disprove an overly optimistic version of the conjecture.
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