Seminar Event Detail

Student Algebraic Geometry

Date:  Friday, January 21, 2022
Location:  2866 East Hall (3:00 PM to 4:00 PM)

Title:  The Kodaira's Embedding Theorem and Applications

Abstract:   We will discuss the proof of Kodaira's embedding theorem which gives us an answer whether a complex manifold can be embedded into a projective space. The statement of the theorem is as follows. A complex manifold $X$ is projective if and only if $X$ admits an integral K√§hler class. The key algebraic input of this proof is using Kodaira's vanishing theorem and the blowup to mimic the proof of projectivity when $X$ is a curve. Time abiding, I will give one interesting application of this theorem which says that the torus $\Pic^{0}(X)$ of a projective manifold $X$ is again projective.

** I will try to avoid talking too much about analysis in detail, but will show some hints of analytic techniques. **


Speaker:  Hyunsuk Kim
Institution:  UM

Event Organizer:     


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