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

Published 7 May 2026 in math.CV, math.AG, and math.DG | (2605.05582v1)

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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