Department of Mathematics,
University of California San Diego
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Math 208: Seminar in Algebraic Geometry
Dr. Wern Yeong
UCLA
A hyperbolicity conjecture for adjoint bundles
Abstract:
A complex manifold X is said to be Brody hyperbolic if it admits no entire curves, which are non-constant holomorphic maps from the complex numbers. When X is a smooth complex projective variety, Demailly introduced an algebraic analogue of this property known as algebraic hyperbolicity. We propose a conjecture on the algebraic hyperbolicity of generic sections of adjoint bundles on X, motivated by Fujita’s freeness conjecture and recent results by Bangere and Lacini on syzygies of adjoint bundles. We present some old and new evidence supporting this conjecture, including when X is any smooth projective toric variety or Gorenstein toric threefold. This is based on joint work with Joaquín Moraga.
Host: Dragos Oprea
May 23, 2025
4:00 PM
APM 7321
Research Areas
Algebraic Geometry****************************
