Fiber Integration on the Demailly Tower

Darondeau, Lionel

Annales de l'Institut Fourier, Tome 66 (2016) no. 1, pp. 29-54.

Le but de ce travail est de fournir une formule d’intégration le long des fibres de la tour de Demailly, évitant l’élimination pas-à-pas des classes de cohomologie horizontales, et permettant des calculs effectifs. Une modification naturelle de la tour de Demailly est introduite et une formule récursive pour la classe de Segre totale au niveau $k$ est obtenue. Ensuite, l’interprétation des classes de Segre individuelles comme des coefficients mêne à une formule de résidus itérés.

The goal of this work is to provide a fiber integration formula on the Demailly tower, that avoids step-by-step elimination of horizontal cohomology classes, and that yields computational effectivity. A natural twist of the Demailly tower is introduced and a recursive formula for the total Segre class at $k$-th level is obtained. Then, by interpreting single Segre classes as coefficients, an iterated residue formula is derived.

Classification : 14C17, 32Q45, 14Q20
Keywords: Demailly tower of logarithmic directed manifold, Gysin homomorphism, Segre classes, iterated Laurent series.
Mot clés : Tour de Demailly logarithmique, morphisme de Gysin, classes de Segre. séries de Laurent itérées.

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