2024/11/11 by Tsz On Mario Chan, Chan, Tsz On Mario
Computer Science · Mathematics · #14B05 (secondary) #32J25 (primary) 51N15 #32Q15 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Complex Variables (math.CV) #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2411.07129
openalex publication_date 2024/11/11 · openalex created_date 2024/11/15 · openalex updated_date 2026/07/28
The effective freeness in Fujita's conjecture states that, for an ample line bundle L on a complex projective manifold X, the adjoint bundle KX⊗ L⊗ m is globally generated when m ≥ dim\mathbb C X + 1. Following the approach of Angehrn and Siu, a solution is provided in this paper via the use of adjoint ideal sheaves, which provide a finer control of the non-integrable loci given by multiplier ideal sheaves, so that one can work directly with the lc singularities and the associated (minimal) lc centres as in the algebraic approaches of Kawamata and Helmke. The substitute for the Nadel or Kawamata-Viehweg vanishing theorem used in previous approaches is an extension theorem based on the techniques developed for the injectivity theorems.