3 papers
math.AG2023
Exceptional collections and phantoms of special Dolgachev surfaces
Ilya Karzhemanov, Ludmil Katzarkov
We provide an explicit description of exceptional collection of maximal length in the derived category for a particular class of elliptic surfaces . The existence of no…
math.AG2012
Unirationality and existence of infinitely transitive models
Fedor Bogomolov, Ilya Karzhemanov, Karine Kuyumzhiyan
We study unirational algebraic varieties and the fields of rational functions on them. We show that after adding a finite number of variables some of these fields admit an infinite…
math.AG2010
Remark on polarized K3 surfaces of genus 36
Ilya Karzhemanov
Smooth primitively polarized surfaces of genus 36 are studied. It is proved that all such surfaces , for which there exists an embedding $\mathrm{R} \hookrightarro…