En utilisant la dualité des cônes positifs, nous montrons que l’application de la transformation polaire de l’analyse convexe aux invariants positivité locaux pour les diviseurs donne des invariants de positivité locaux intéressants et nouveaux pour les courbes. Ces nouveaux invariants ont de belles propriétés similaires à celles des diviseurs. En particulier, cela nous permet d’établir un critère d’amplitude de type Seshadri pour les courbes mobiles, et de caractériser les composantes divisorielles du locus non-Kähler d’une classe grande.
Using the duality of positive cones, we show that applying the polar transform from convex analysis to local positivity invariants for divisors gives interesting and new local positivity invariants for curves. These new invariants have nice properties similar to those for divisors. In particular, this enables us to establish a Seshadri type ampleness criterion for movable curves, and give a characterization of the divisorial components of the non-Kähler locus of a big class.
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@article{AFST_2020_6_29_2_247_0,
author = {McCleerey, Nicholas and Xiao, Jian},
title = {Polar transform and local positivity for curves},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {247--269},
publisher = {Universit\'e Paul Sabatier, Toulouse},
volume = {Ser. 6, 29},
number = {2},
year = {2020},
doi = {10.5802/afst.1631},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/afst.1631/}
}
TY - JOUR AU - McCleerey, Nicholas AU - Xiao, Jian TI - Polar transform and local positivity for curves JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2020 SP - 247 EP - 269 VL - 29 IS - 2 PB - Université Paul Sabatier, Toulouse UR - http://archive.numdam.org/articles/10.5802/afst.1631/ DO - 10.5802/afst.1631 LA - en ID - AFST_2020_6_29_2_247_0 ER -
%0 Journal Article %A McCleerey, Nicholas %A Xiao, Jian %T Polar transform and local positivity for curves %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2020 %P 247-269 %V 29 %N 2 %I Université Paul Sabatier, Toulouse %U http://archive.numdam.org/articles/10.5802/afst.1631/ %R 10.5802/afst.1631 %G en %F AFST_2020_6_29_2_247_0
McCleerey, Nicholas; Xiao, Jian. Polar transform and local positivity for curves. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 2, pp. 247-269. doi : 10.5802/afst.1631. http://archive.numdam.org/articles/10.5802/afst.1631/
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