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NONUNIFORMLY FLAT AFFINE ALGEBRAIC HYPERSURFACES

Part of: Differential operators in several variables Pluripotential theory Holomorphic functions of several complex variables

Published online by Cambridge University Press:  02 April 2019

VAMSI PRITHAM PINGALI  and
DROR VAROLIN
VAMSI PRITHAM PINGALI
Affiliation:
Department of Mathematics, Indian Institute of Science, Bangalore - 560012, India email vamsipingali@iisc.ac.in
DROR VAROLIN
Affiliation:
Department of Mathematics, Stony Brook University, Stony Brook, NY 11794-3651, USA email dror@math.stonybrook.edu
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Abstract

The relationship between interpolation and separation properties of hypersurfaces in Bargmann–Fock spaces over $\mathbb{C}^{n}$ is not well understood except for $n=1$. We present four examples of smooth affine algebraic hypersurfaces that are not uniformly flat, and show that exactly two of them are interpolating.

MSC classification

Primary: 32A36: Bergman spaces 32U05: Plurisubharmonic functions and generalizations 32W50: Other partial differential equations of complex analysis
Type
Article
Information
Nagoya Mathematical Journal , Volume 241 , March 2021 , pp. 1 - 43
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Copyright
© 2019 Foundation Nagoya Mathematical Journal

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Footnotes

Vamsi Pritham Pingali is partially supported by the Young Investigator Award and by grant F.510/25/CAS-II/2018(SAP-I) from UGC (Govt. of India).

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