Pluricanonical systems of projective varieties of general type

TL;DR

This paper proves that for smooth projective varieties of general type, a uniform multiple of the canonical divisor yields a birational map, confirming Severi's conjecture using AZD theory and subadjunction formulas.

Contribution

It establishes a uniform bound for pluricanonical systems of general type varieties, advancing the understanding of their birational geometry.

Findings

Existence of a universal integer _n for birationality

Affirmative answer to Severi's conjecture

Application of AZD and subadjunction techniques

Abstract

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.