On the canonical threefolds with strictly nef anticanonical divisors

Details On the canonical threefolds with strictly nef anticanonical divisors On the canonical threefolds with strictly nef anticanonical divisors

1999-12-31

arxiv.org/abs/math/9912241v1

Mathematics

Algebraic Geometry

21 pages, LaTeX

Scientific paper

Any ample Cartier divisor D on a projective variety X is strictly nef (i.e. D.C>0 for any effective curve C on X). In general, the converse statement does not hold. But this is conjectured to be true for anticanonical divisors. The present paper establishes this fact for normal complex projective threefolds with canonical singularities. This result extends several previously known special cases. The proof rests mainly on sophisticated techniques of three dimensional birational geometry developed in the last two decades.

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