##### Department of Mathematics,

University of California San Diego

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### Algebraic Geometry Seminar

## Nikolay Buskin

#### UCSD

## Every rational Hodge isometry between two K3 surfaces is algebraic

##### Abstract:

We prove that cohomology classes in $H^{2,2}(S_1\times S_2)$ of Hodge isometries $$\psi \colon H^2(S_1,\mathbb Q)\rightarrow H^2(S_2,\mathbb Q)$$ between any two projective complex $K3$ surfaces $S_1$ and $S_2$ are polynomials in Chern classes of coherent analytic sheaves. Consequently, the cohomology class of $\psi$ is algebraic This proves a conjecture of Shafarevich announced at ICM in 1970.

Organizer: James McKernan

### October 14, 2016

### 4:30 PM

### AP&M 5829

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