On freeness theorem of the adjoint bundle on a normal surface
Abstract
Description
We extend Reider's freeness criterion to normal surfaces of characteristic 0.
Let Y be a normal surface.
Let D be a nef divisor on Y such that K_Y+D is a Cartier divisor.
Let x be a point on Y.
If x is a base point of |K_Y+D| and D^2>δ_x (δ_x is determined by x, δ_x <= 4) then there exists a non zero effective divisor E on Y passing through x such that
0 <= DE <= δ_x /2,
DE - δ_x /4 <= E^2 <= (DE)^2 / D^2,
E^2 < 0 if DE=0.
AmS-TeX 2.1 + 4 PostScript files, 29 pages
AmS-TeX 2.1 + 4 PostScript files, 29 pages