Return to Colloquia & Seminar listing
Clustered families and applications to Lang-type Conjectures
Algebraic Geometry and Number Theory| Speaker: | Izzet Coskun, UIC |
| Location: | Zoom |
| Start time: | Wed, Feb 2 2022, 1:00PM |
Description
Lang in an attempt to generalize Mordell's Conjecture/Faltings'
Theorem to higher dimensions made a series of far reaching conjectures
concerning the arithmetic and hyperbolicity of projective varieties. In
this talk, I will describe several Lang-type results for algebraic
hyperbolicity on hypersurfaces. Let X in P^n be a very general
hypersurface of degree d. For example, if 2d \geq 3n +2, then X is
algebraically hyperbolic outside the locus covered by lines. If 2d \geq
3n, then X contains lines but no other rational curves. This is joint
work with Eric Riedl.