Pluricanonical systems of projective varieties of general type

Details Pluricanonical systems of projective varieties of general type Pluricanonical systems of projective varieties of general type

1999-09-03

arxiv.org/abs/math/9909021v10

Mathematics

Algebraic Geometry

27pages, rewritten so that algebraists can read easily

Scientific paper

We prove that there exists a positive integer $\nu_{n}$ depending only on $n$ such that for every smooth projective $n$-fold of general type $X$ defined over {\bf C}, $\mid mK_{X}\mid$ gives a birational rational map from $X$ into a projective space for every $m\geq \nu_{n}$. This theorem gives an affirmative answer to Severi's conjecture. The key ingredients of the proof are the theory of AZD which was originated by the aurhor and the subadjunction formula for AZD's of logcanoncial divisors.

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