EVENT: Pure Mathematics Seminar
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Pure Mathematics Seminar : Triangulated topological manifolds and special algebraic varieties |
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Abstract: A simplicial complex K gives rise to a Stanley-Reisner ring A and a projective scheme X inside some projective space.
The scheme X “looks like” K as it is the union, over all faces F in K, of linear subspaces of dimension dim F. These intersect as
in K. If K is a combinatorial manifold (with boundary) then, if X is smoothable, it deforms to a special algebraic variety. (Technically:
the Kodaira dimension is not positive.) E.g. spheres correspond to Calabi-Yau manifolds (elliptic curves, K3-surfaces, ...) and tori
to abelian varieties. There are a lot of interesting simplicial complexes and they lead to interesting algebraic geometry. I will explain
this connection and give examples where K is a special triangulated sphere, torus, ball and Möbius strip.
Speaker(s) |
Jan Christophersen (University of Oslo)
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Location |
Mathematics Lecture Room 1
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Contact |
Stephanie Gawne
<[email protected]>
: 3393
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Start |
Wed, 28 Mar 2012 16:00
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End |
Wed, 28 Mar 2012 17:00
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Submitted by |
Stephanie Gawne <[email protected]>
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Last Updated |
Fri, 23 Mar 2012 09:40
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