TY - JOUR
A2 - Jaballah, A.
A2 - Dascalescu, S.
A2 - Rapinchuk, A.
A2 - Airault, H.
A2 - Kelarev, A. V.
AU - Zhang, Jing
PY - 2013
DA - 2013/03/20
TI - A New Criterion for Affineness
SP - 786576
VL - 2013
AB - We show that an irreducible quasiprojective variety Y of dimension d≥1 defined over an algebraically closed field with characteristic zero is an affine variety if and only if Hi(Y,Y) = 0 and Hi (Y,Y(−Z)) = 0 for all i>0, Z=H∩Y, where H is any hypersurface with sufficiently large degree. A direct application is that an irreducible quasiprojective variety Y over ℂ is a Stein variety if it satisfies the two vanishing conditions. Here, all sheaves are algebraic.
SN - null
UR - https://doi.org/10.1155/2013/786576
DO - 10.1155/2013/786576
JF - ISRN Algebra
PB - Hindawi Publishing Corporation
KW -
ER -