3:30 pm Tuesday, October 30, 2012
Jr Geometry: The hard Lefschetz theorem without the Hodge theory by Yuecheng Zhu (UT Austin) in RLM 9.166
I am going to sketch a proof of the hard Lefschetz theorem without the Hodge theory (i.e. harmonic analysis). The basic idea is a double induction on the existence of polarized (mixed) Hodge structures for projective varieties of dimension n and the hard Lefschetz theorem for smooth projective varieties of dimension n. I will basically focus on one part, how to get the polarized Hodge structure from the hard Lefschetz theorem. There is virtue about this indirect proof. On the one hand, it can be generalized (over other fields, or singular varieties). On the other hand, I can introduce some of the basic tools for studying the topology of complex algebraic varieties. Submitted by
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