## Doctoral Dissertations

Dissertations that have an embargo placed on them will not be available to anyone until the embargo expires.

#### Document Type

Open Access Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

Mathematics

2016

May

Eyal Markman

#### Subject Categories

Algebraic Geometry

#### Abstract

Consider any rational Hodge isometry

$\psi:H^2(S_1,\QQ)\rightarrow H^2(S_2,\QQ)$ between any two K\"ahler $K3$

surfaces $S_1$ and $S_2$. We prove that the cohomology class of $\psi$ in $H^{2,2}(S_1\times S_2)$

is a polynomial in Chern classes of coherent analytic sheaves

over $S_1 \times S_2$. Consequently, the cohomology class of $\psi$ is algebraic

whenever $S_1$ and $S_2$ are algebraic.