Scientific Staff

Ilya Karzhemanov
Position
Project Researcher (from 2013/11/01 )
Research Field
Mathematics
E-Mail
<ilya.karzhemanov _at_ ipmu.jp> 
PHOTO

Last Update 2014/05/08 16:37:10

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) multiplicity-type 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 differential-geometric 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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