Complexity of singular Reinhardt domains and the regularity of the Bergman projection

Abstract: We consider a large class of singular Reinhardt domains in C n and develop a general framework from which we may understand the L p -regularity of their Bergman projections. The domains in this class may be realized as quotients of simpler domains under the action of a finite group of biholomorphic automorphisms. It is shown that the range of Bergman L p -boundedness is closely connected to the ”arithmetic complexity” of the original domain, a notion that will be made precise. We then look at a spiritually similar domain falling outside of this class – one which was previously known to have a transcendental Bergman kernel function. Despite this knowledge, we obtain an explicit kernel formula involving logarithmic terms for this domain. This talk combines various projects of the speaker with collaborators Chase Bender, Debraj Chakrabarti and Meera Mainkar.

complex variables

Audience: researchers in the discipline

Virtual East-West Several Complex Variables Seminar

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