##### Department of Mathematics,

University of California San Diego

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### Math 208 - Algebraic Geometry Seminar

## Ljudmila Kamenova

#### Stony Brook University

## Algebraic non-hyperbolicity of hyperkahler manifolds

##### Abstract:

A projective manifold is algebraically hyperbolic if the degree of any curve is bounded from above by its genus times a constant, which is independent from the curve. This is a property which follows from Kobayashi hyperbolicity. We prove that hyperkahler manifolds are not algebraically hyperbolic when the Picard rank is at least 3, or if the Picard rank is 2 and the SYZ conjecture on existence of Lagrangian fibrations is true. We also prove that if the automorphism group of a hyperkahler manifold is infinite, then it is algebraically non-hyperbolic. \\ \\ These results are a joint work with Misha Verbitsky.

Host: Elham Izadi

### February 12, 2021

### 11:00 AM

### Contact David Stapleton, dstapleton@ucsd.edu, for zoom access

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