Lecture notes on generalized Monge-Amp\`ere equations and subvarieties

Gao Chen

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Lecture notes on generalized Monge-Amp\`ere equations and subvarieties

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arxiv 2210.01345 v1 pith:NHI46ADI submitted 2022-10-04 math.DG math.AGmath.CV

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keywords equationsgeneralizedlecturemonge-ampnotesresultssubvarietiesaugust

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These are the lecture notes for the Morningside Center of Mathematics Geometry Summer School on August 15-20, 2022. These lectures sketch the results by Yau, Demailly-Paun, the author, and Datar-Pingali about generalized Monge-Amp\`ere equations and subvarieties and aim to use these results to study the Hodge conjecture.

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