[Sur le genre des surfaces réductibles et dégénérescences des surfaces]
Nous étudions une surface projective réductible avec des singularités dites Zappatiques, qui sont une généralisation des croisements normaux. Nous calculons d’abord le -genre de , c’est-à-dire la dimension de l’espace vectoriel des sections globales du faisceau dualisant sur . Nous démontrons après que, si est lissifiable, c’est-à-dire si est la fibre centrale d’une famille plate paramétrée par un disque, à fibre générale lisse, alors le -genre des fibres est constant.
We deal with a reducible projective surface with so-called Zappatic singularities, which are a generalization of normal crossings. First we compute the -genus of , i.e. the dimension of the vector space of global sections of the dualizing sheaf . Then we prove that, when is smoothable, i.e. when is the central fibre of a flat family parametrized by a disc, with smooth general fibre, then the -genus of the fibres of is constant.
Keywords: Degenerations of surfaces, singularities, birational geometry, topological invariants
Mot clés : dégénérescence de surfaces, singularités, géométrie birationnelle, invariants topologiques
Calabri, Alberto 1 ; Ciliberto, Ciro 2 ; Flamini, Flaminio 3 ; Miranda, Rick 4
@article{AIF_2007__57_2_491_0,
author = {Calabri, Alberto and Ciliberto, Ciro and Flamini, Flaminio and Miranda, Rick},
title = {On the genus of reducible surfaces and degenerations of surfaces},
journal = {Annales de l'Institut Fourier},
pages = {491--516},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {57},
number = {2},
year = {2007},
doi = {10.5802/aif.2266},
mrnumber = {2310949},
zbl = {1125.14018},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2266/}
}
TY - JOUR AU - Calabri, Alberto AU - Ciliberto, Ciro AU - Flamini, Flaminio AU - Miranda, Rick TI - On the genus of reducible surfaces and degenerations of surfaces JO - Annales de l'Institut Fourier PY - 2007 SP - 491 EP - 516 VL - 57 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2266/ DO - 10.5802/aif.2266 LA - en ID - AIF_2007__57_2_491_0 ER -
%0 Journal Article %A Calabri, Alberto %A Ciliberto, Ciro %A Flamini, Flaminio %A Miranda, Rick %T On the genus of reducible surfaces and degenerations of surfaces %J Annales de l'Institut Fourier %D 2007 %P 491-516 %V 57 %N 2 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2266/ %R 10.5802/aif.2266 %G en %F AIF_2007__57_2_491_0
Calabri, Alberto; Ciliberto, Ciro; Flamini, Flaminio; Miranda, Rick. On the genus of reducible surfaces and degenerations of surfaces. Annales de l'Institut Fourier, Tome 57 (2007) no. 2, pp. 491-516. doi : 10.5802/aif.2266. https://aif.centre-mersenne.org/articles/10.5802/aif.2266/
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