Ilya Karzhemanov

Last Update 2019/04/15
My research interests are in algebraic, especially birational, geometry. I am interested in developing numerical criteria, which should be typical for rational, or more specically, homegeneous/toric varieties. Among such invariants are (asymptotic) multiplicitytype functions, constructed with respect to a given line bundle L on an algebraic variety X, i.e. to any point p on X the function (say m) in question associates (appropriately averaged) multiplicity m(p) at p of various (maybe not all) global sections of L. In case m is a sort of a distribution on X (e.g. m is constant), one might expect X to be“ close to homogeneous space,” in particular stable (for one of the (or any) kinds of known differentialgeometric versions of stability). On the other hand, the“ nonhomogeneous” behavior of m should give an obstruction for X to be rational.
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