Sheaves associated to holomorphic first integrals

Zamora, Alexis García. "Sheaves associated to holomorphic first integrals." Annales de l'institut Fourier 50.3 (2000): 909-919. <http://eudml.org/doc/75443>.

@article{Zamora2000,
abstract = {Let $\{\cal F\}: L \rightarrow TS$ be a foliation on a complex, smooth and irreducible projective surface $S$, assume $\{\cal F\}$ admits a holomorphic first integral $f:S \rightarrow \{\Bbb P\}^1$. If $h^0(S,\{\cal O\}_S(-n\{\cal K\}_S))&gt;0$ for some $n\ge 1$ we prove the inequality: $(2n-1)(g-1) \le h^1(S, \{\cal L\}^\{\prime -1\}(-(n-1)K_S)) +h^0 (S, \{\cal L\}^\prime ) +1$. If $S$ is rational we prove that the direct image sheaves of the co-normal sheaf of $\{\cal F\}$ under $f$ are locally free; and give some information on the nature of their decomposition as direct sum of invertible sheaves.},
author = {Zamora, Alexis García},
journal = {Annales de l'institut Fourier},
keywords = {holomorphic foliations; first integrals},
language = {eng},
number = {3},
pages = {909-919},
publisher = {Association des Annales de l'Institut Fourier},
title = {Sheaves associated to holomorphic first integrals},
url = {http://eudml.org/doc/75443},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Zamora, Alexis García
TI - Sheaves associated to holomorphic first integrals
JO - Annales de l'institut Fourier
PY - 2000
PB - Association des Annales de l'Institut Fourier
VL - 50
IS - 3
SP - 909
EP - 919
AB - Let ${\cal F}: L \rightarrow TS$ be a foliation on a complex, smooth and irreducible projective surface $S$, assume ${\cal F}$ admits a holomorphic first integral $f:S \rightarrow {\Bbb P}^1$. If $h^0(S,{\cal O}_S(-n{\cal K}_S))&gt;0$ for some $n\ge 1$ we prove the inequality: $(2n-1)(g-1) \le h^1(S, {\cal L}^{\prime -1}(-(n-1)K_S)) +h^0 (S, {\cal L}^\prime ) +1$. If $S$ is rational we prove that the direct image sheaves of the co-normal sheaf of ${\cal F}$ under $f$ are locally free; and give some information on the nature of their decomposition as direct sum of invertible sheaves.
LA - eng
KW - holomorphic foliations; first integrals
UR - http://eudml.org/doc/75443
ER -