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Homology classes in algebraic varieties: nef, effective, and prime
Special Events| Speaker: | June Huh, University of Michigan |
| Location: | 2112 MSB |
| Start time: | Mon, Apr 28 2014, 4:10PM |
Description
The homology group of an algebraic variety is an abelian group equipped
with several additional structures. It contains the set of primes, the
homology classes of subvarieties. It contains the semigroup of effective
classes, the nonnegative linear combinations of primes. It contains the
semigroup of nef classes, the classes which intersect all primes of
complementary dimension nonnegatively. We will see how these subsets look
like in a particular algebraic variety, the one associated to the polytope
`permutahedron'. The semigroups in this case have tractable structures,
while the distribution of primes is more mysterious and related to some
deep combinatorial conjectures on matroids.