Revised Demailly's Affineness Criterion and Algebraization of Entire Grauert Tubes

Kyobeom Song

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arXiv · 2605.05582

Revised Demailly's Affineness Criterion and Algebraization of Entire Grauert Tubes

Kyobeom Song

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Abstract

We provide a partial answer to Burns' 1982 conjecture on the affineness of entire Grauert tubes: the complement of a codimension-one subset of an entire Grauert tube is affine. This result is obtained by establishing a generalized version of Demailly's criterion for affineness of Stein manifolds, which may be of independent interest.

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Kyobeom Song. 2026-05-07. Revised Demailly's Affineness Criterion and Algebraization of Entire Grauert Tubes. https://arxiv.org/abs/2605.05582

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