K-stability and space sextic curves of genus three

Antoine Pinardin; Ivan Cheltsov; Oliver Li; Sione Ma'u

K-stability and space sextic curves of genus three

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arxiv 2404.07803 v1 pith:M6SV3GC5 submitted 2024-04-11 math.AG

Ivan Cheltsov , Oliver Li , Sione Ma'u , Antoine Pinardin This is my paper · ORCID

classification math.AG

keywords genusspacethreethreefoldsalongblowingcurvecurves

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We study Fano threefolds that can be obtained by blowing up the three-dimensional projective space along a smooth curve of degree six and genus three. We produce many new K-stable examples of such threefolds, and we describe all finite groups that can act faithfully on them.

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K-stability of Fano 3-folds in the World of Null-A
math.AG 2025-05 accept novelty 6.0 of 10

Every smooth Fano 3-fold that fails Condition (A), meaning it has a finite abelian automorphism group with no fixed point, is K-polystable except for eight explicit deformation families.

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