Open problems on structure of positively curved projective varieties

Matsumura, Shin-ichi

Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, AMAZER, Volume 31 (2022) no. 3, pp. 1011-1029.

We provide supplements and open problems related to structure theorems for maximal rationally connected fibrations of certain positively curved projective varieties, including smooth projective varieties with semi-positive holomorphic sectional curvature, pseudo-effective tangent bundle, and nef anti-canonical divisor.

Nous fournissons des suppléments et des problèmes ouverts liés aux théorèmes de structure pour les fibrations maximales rationnellement connectées de certaines variétés projectives à courbure positive, y compris les variétés projectives lisses avec une courbure de section holomorphe semi-positive, un faisceau tangent pseudo-efficace et un diviseur anticanonique nef.

Classification: 32J25, 53C25, 14E30
Mots-clés : Rational curves, Maximal rationally connected fibrations, Albanese maps, Structure theorems, Holomorphic sectional curvatures, Pseudo-effective tangent bundles, Nef anti-canonical divisors, klt pairs.

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