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.
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.
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.
@article{AFST_2022_6_31_3_1011_0, author = {Matsumura, Shin-ichi}, title = {Open problems on structure of positively curved projective varieties}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {1011--1029}, publisher = {Universit\'e Paul Sabatier, Toulouse}, volume = {Ser. 6, 31}, number = {3}, year = {2022}, doi = {10.5802/afst.1712}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/afst.1712/} }
TY - JOUR AU - Matsumura, Shin-ichi TI - Open problems on structure of positively curved projective varieties JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2022 SP - 1011 EP - 1029 VL - 31 IS - 3 PB - Université Paul Sabatier, Toulouse UR - http://archive.numdam.org/articles/10.5802/afst.1712/ DO - 10.5802/afst.1712 LA - en ID - AFST_2022_6_31_3_1011_0 ER -
%0 Journal Article %A Matsumura, Shin-ichi %T Open problems on structure of positively curved projective varieties %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2022 %P 1011-1029 %V 31 %N 3 %I Université Paul Sabatier, Toulouse %U http://archive.numdam.org/articles/10.5802/afst.1712/ %R 10.5802/afst.1712 %G en %F AFST_2022_6_31_3_1011_0
Matsumura, Shin-ichi. Open problems on structure of positively curved projective varieties. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 31 (2022) no. 3, pp. 1011-1029. doi : 10.5802/afst.1712. http://archive.numdam.org/articles/10.5802/afst.1712/
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