[Applications polaires toriques, croisements normaux et volumes mixtes]
Given a hypersurface in a complex projective space, we prove that the Chern–Schwartz–MacPherson class of a certain open set, namely the complement of the union of the hypersurface and the coordinate hyperplanes, is given (up to sign) by the multidegrees of associated toric polar map, in two particular cases: normal crossings with the coordinate hyperplanes and a nondegeneracy condition with respect to the Newton polytope. In the latter case, we also recover the multidegrees from mixed volumes.
Étant donné une hypersurface dans un espace projectif complexe, nous prouvons que la classe de Chern–Schwartz–MacPherson d’un certain ensemble ouvert, à savoir le complément de l’union de l’hypersurface et des hyperplans coordonnés, est donnée (à un signe près) par les multidegrés de l’application polaire torique associée, dans deux cas particuliers : les croisements normaux avec les hyperplans coordonnés et une condition de non dégénérescence par rapport au polytope de Newton. Dans ce dernier cas, nous récupérons également les multidegrés à partir de volumes mixtes.
Révisé le :
Accepté le :
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Thiago Fassarella 1 ; Nivaldo Medeiros 1 ; Rodrigo Salomão 1
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@article{CRMATH_2025__363_G5_511_0,
author = {Thiago Fassarella and Nivaldo Medeiros and Rodrigo Salom\~ao},
title = {Toric polar maps, normal crossings and mixed volumes},
journal = {Comptes Rendus. Math\'ematique},
pages = {511--522},
publisher = {Acad\'emie des sciences, Paris},
volume = {363},
year = {2025},
doi = {10.5802/crmath.734},
language = {en},
}
TY - JOUR AU - Thiago Fassarella AU - Nivaldo Medeiros AU - Rodrigo Salomão TI - Toric polar maps, normal crossings and mixed volumes JO - Comptes Rendus. Mathématique PY - 2025 SP - 511 EP - 522 VL - 363 PB - Académie des sciences, Paris DO - 10.5802/crmath.734 LA - en ID - CRMATH_2025__363_G5_511_0 ER -
Thiago Fassarella; Nivaldo Medeiros; Rodrigo Salomão. Toric polar maps, normal crossings and mixed volumes. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 511-522. doi : 10.5802/crmath.734. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.734/
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