Improvement of Grauert-Riemenschneider's theorem for a normal surface

@article{Giraud1982,
abstract = {Let $\widetilde\{X\}$ be a desingularization of a normal surface $X$. The group Pic$(\widetilde\{X\})$ is provided with an order relation $L \underline\{\gg \} 0$, defined by $L$. $V\le 0$ for any effective exceptional divisor $V$. Comparing to the usual order relation we define the ceiling of $L$ which is an exceptional divisor. This notion allows us to improve the usual vanishing theorem and we deduce from it a numerical criterion for rationality and a genus formula for a curve on a normal surface; the difficulty lies in the case of a Weil divisor which is not a Cartier divisor.},
author = {Giraud, Jean},
journal = {Annales de l'institut Fourier},
keywords = {effective exceptional divisor; vanishing theorem; numerical criterion for rationality; genus formula; Weil divisor; Cartier divisor; Picard group},
language = {eng},
number = {4},
pages = {13-23},
publisher = {Association des Annales de l'Institut Fourier},
title = {Improvement of Grauert-Riemenschneider's theorem for a normal surface},
url = {http://eudml.org/doc/74556},
volume = {32},
year = {1982},
}

TY - JOUR
AU - Giraud, Jean
TI - Improvement of Grauert-Riemenschneider's theorem for a normal surface
JO - Annales de l'institut Fourier
PY - 1982
PB - Association des Annales de l'Institut Fourier
VL - 32
IS - 4
SP - 13
EP - 23
AB - Let $\widetilde{X}$ be a desingularization of a normal surface $X$. The group Pic$(\widetilde{X})$ is provided with an order relation $L \underline{\gg } 0$, defined by $L$. $V\le 0$ for any effective exceptional divisor $V$. Comparing to the usual order relation we define the ceiling of $L$ which is an exceptional divisor. This notion allows us to improve the usual vanishing theorem and we deduce from it a numerical criterion for rationality and a genus formula for a curve on a normal surface; the difficulty lies in the case of a Weil divisor which is not a Cartier divisor.
LA - eng
KW - effective exceptional divisor; vanishing theorem; numerical criterion for rationality; genus formula; Weil divisor; Cartier divisor; Picard group
UR - http://eudml.org/doc/74556
ER -