When a compact complex manifold is given as the vanishing locus of polynomial equations, its singular cohomology groups possess natural direct-sum decompositions called Hodge structures. These Hodge structures strongly influence the topology of the variety; for instance, their mere existence implies that the odd-degree cohomology groups have even rank. I will explain what these structures are and how they lead to nice discrete invariants of algebraic varieties, such as Hodge numbers and Hodge diamonds. I will also discuss connections to the Grothendieck ring of varieties. Speaker(s): James Hotchkiss (UM)
Building: | East Hall |
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Event Type: | Workshop / Seminar |
Tags: | Mathematics |
Source: | Happening @ Michigan from Department of Mathematics |