##### Department of Mathematics,

University of California San Diego

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### RTG Colloquium

## Nikolay Buskin

#### UCSD

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

##### Abstract:

We present a proof of the fact that given a Hodge isometry Psi between the rational second cohomology of two Kahler K3 surfaces $S_1$ and $S_2$, we can find a finite sequence of K3 surfaces and analytic (2, 2)-classes supported on successive products, such that the isometry Psi is the convolution of these classes. The proof of this fact implies that for projective K3 surfaces $S_1$, $S_2$ the class of Psi is algebraic. This proves a conjecture of I. Shafarevich.

Organizer: James McKernan

### May 24, 2017

### 3:00 PM

### AP&M 2402

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