Effective freeness of adjoint line bundles

Abstract

In this note we establish a new Fujita-type effective bound for the base point freeness of adjoint line bundles on a compact complex projective manifold of complex dimension $n$. The bound we obtain (approximately) differs from the linear bound conjectured by Fujita only by a factor of the cube root of $n$. As an application, a new effective statement for pluricanonical embeddings is derived.

13 pages, AMS-LaTeX

References in corpus (2)

• Remarks on Ein-Lazarsfeld criterion of spannedness of adjoint bundles of polarized threefolds
• Freeness of adjoint linear systems on threefolds with terminal Gorenstein singularities or some quotient singularities

Cited by in corpus (5)

• Effective results for complex hyperbolic manifolds
• Seshadri Constants and Fujita's Conjecture via Positive Characteristic Methods
• On Fujita's freeness conjecture in dimension 5
• Uniformly effective boundedness of Shafarevich Conjecture-type for families of canonically polarized manifolds
• Effective global generation on varieties with numerically trivial canonical class