The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on December 17, 2019  at 2:00 p.m. in room 478 of IMI.
A talk on:

Algebraic theory for continuity for meromorphic functions

will be delivered by Antoni Rangachev, University of Chicago, IMI-BAS.

Everybody is invited.

Abstract. For a reduced complex analytic variety X and a rational number α between 0 and 1 I will show that the meromorphic functions on X that are Holder continuous with exponent α form a coherent sheaf that sits between the structure sheaf of X and its normalization. In fact, there are finitely many α that matter. For exponent α = 1 the result recovers the Lipschitz saturation considered by Pham-Teissier and Zariski. The proof uses the Riemann extension theorem, which allows us to turn inequalities into integral dependence relations, rational powers of ideals and Rees’ valuation theorem.