2008/02/01 by Simone Diverio, Diverio, Simone
Mathematics · #14F99 #32Q45 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.0802.0045
openalex publication_date 2008/02/01 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
Let X\⊂ mathbb Pn+1 be a smooth complex projective hypersurface. In\nthis paper we show that, if the degree of X is large enough, then there exist\nglobal sections of the bundle of invariant jet differentials of order n on\nX, vanishing on an ample divisor. We also prove a logarithmic version,\neffective in low dimension, for the log-pair ( mathbb Pn,D), where D is a\nsmooth irreducible divisor of high degree. Moreover, these result are sharp,\n\i.e. one cannot have such jet differentials of order less than n.\n