Pluricanonical systems of projective varieties of general type

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}, $\mid m{K}_X\mid$ gives a birational rational map from $X$ into a projective space for every $m\ge {\nu }_n$. 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.

27pages, rewritten so that algebraists can read easily

References in corpus (2)

• Invariance of Plurigenera
• Finite Generation of Canonical Rings

Cited by in corpus (8)

• Extension of log pluricanonical forms from subvarieties
• Pluricanonical systems of projective 3-folds of general type
• Boundedness of moduli of varieties of general type
• Pluri-canonical maps of varieties of maximal Albanese dimension in positive characteristic
• Varieties of general type with doubly exponential asymptotics
• Pluricanonical maps for threefolds of general type
• On explicit birational geometry for minimal n-folds of canonical dimension n-1
• Effective birationality of pluricanonical systems