MATH 257y Techniques of Pluricanonical Sections and
Jet Differentials of Complex Manifolds
Fall 2019

Place: Science Center 222
Time: Tuesdays, Thursdays, 3 p.m. - 4:15 p.m.

Instructor: Professor Yum-Tong Siu   (e-mail:
Office Hours: Tuesdays, Thursdays 1:30 p.m. - 3 p.m., Science Center 511

Syllabus:   A discussion of recent techniques and results and open problems involving holomorphic pluricanonical sections and jet differentials of complex manifolds.
Topics: The techniques introduced for the deformational invariance of plurigenera and the solution of a number of conjectures on optimal constants in analysis arising from such techniques. The analytic approach to the finite generation of the canonical ring and the abundance conjecture. The hyperbolicty of a generic high-degree complex hypersurface in a complex projective space and more generally the second main theorem in Nevanlinna theory for an entire holomorphic curve in a complex projective space and its counting function for a smooth complex hypersurface.