2016/06/24 by Jeremy Berquist, Berquist, Jeremy
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Meromorphic and Entire Functions #Polynomial and algebraic computation #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.1606.07679
openalex publication_date 2016/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The classical Kodaira Vanishing Theorem states that Hi(X, \ωX \⊗\nL) = 0 for i > 0, where X is a smooth projective variety over C and L is an\nample line bundle on X. We prove an analogous vanishing result under the\nassumption that X is a semi-smooth projective variety over C. This is done by\npassing to the normalization of X, which is a smooth projective variety when X\nis semi-smooth. The classical vanishing result is proved using a cyclic cover.\nTherefore we include a proof that the cyclic cover of a demi-normal variety is\nagain demi-normal.\n