Lecture notes on generalized Monge-Amp\`ere equations and subvarieties
Gao Chen
TL;DR
This paper provides lecture notes on generalized Monge-Ampère equations and subvarieties, summarizing key results by leading mathematicians to explore their implications for the Hodge conjecture.
Contribution
It compiles and explains recent advances in generalized Monge-Ampère equations and their applications to algebraic geometry and the Hodge conjecture.
Findings
Summarizes Yau, Demailly-Paun, and others' results
Links Monge-Ampère equations to subvarieties
Aims to advance understanding of the Hodge conjecture
Abstract
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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Taxonomy
TopicsGeometry and complex manifolds · Algebraic Geometry and Number Theory · Geometric Analysis and Curvature Flows