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Clustered families and applications to Lang-type Conjectures
Algebraic Geometry| Speaker: | Izzet Coskun, UIC |
| Location: | Zoom |
| Start time: | Wed, Feb 2 2022, 1:00PM |
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.