Algebraic Geometry Seminar
Lucas Mioranci
UIC
Algebraic hyperbolicity of very general hypersurfaces in homogeneous varieties
Abstract: A complex projective variety $X$ is algebraically hyperbolic if there exists an ample divisor $H$ and a real number $\epsilon > 0$ such that the geometric genus $g(C)$ and the degree of any integral curve $C\subset X$ satisfy the inequality
\[ 2g(C) - 2\ge \epsilon \deg_H (C). \]
The algebraic hyperbolicity is an important property to characterize varieties of general type, and it is connected to famous conjectures such as the Lang Conjectures and Green-Griffiths Conjecture.
By building on recent work, I classify algebraic hyperbolic hypersurfaces in homogeneous varieties, thus obtaining explicit bounds for the hyperbolicity in plenty of open cases, including Grassmannians, flag varieties, and their products.
Monday October 23, 2023 at 3:00 PM in 636 SEO