Sheaf of pseudoanalytic functions and differential forms on complex manifolds

Author: Irakli Sikharulidze
Keywords: pseudoanalytic function, generalized analytic function, sheaf, Čech cohomology, Serre-type duality, Riemann-Roch analogue
Annotation:

Sheaves of generalized analytic functions and differential forms on a Riemann surface are considered; several propositions regarding them are proven; Čech cohomology groups of these sheaves are characterized. A proof of a Serre-type duality theorem that relates zeroth and first cohomology groups of the sheaf of generalized analytic functions and differential forms on a compact Riemann surface is given along with a proof of an analogue of the Riemann-Roch theorem for pseudoanalytic functions; aforementioned proof utilizes facts about Čech cohomology with values in a sheaf. The way these sheaves are defined makes it possible to consider them on a complex manifold of any dimension. The constrcutions and proofs mentioned above are new.

Lecture files:

ფსევდანალიზურ ფუნქციათა კონა კელერისა და რიმანის მრავალსახეობებზე [ka]
ფსევდანალიზურ ფუნქციათა კონა კელერისა და რიმანის მრავალსახეობებზე [ka]