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EVENT: Pure Mathematics Seminar

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Today's date is Friday, March 29, 2024
Pure Mathematics Seminar : Triangulated topological manifolds and special algebraic varieties Other events...
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)
Location Mathematics Lecture Room 1
Contact Stephanie Gawne <[email protected]> : 3393
Start Wed, 28 Mar 2012 16:00
End Wed, 28 Mar 2012 17:00
Submitted by Stephanie Gawne <[email protected]>
Last Updated Fri, 23 Mar 2012 09:40
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