Compositio Mathematica



Logarithmic Vanishing Theorems and Arakelov–Parshin Boundedness for Singular Varieties


Sándor J. Kovács a1
a1 Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98103, U.S.A. E-mail: kovacs@math.washington.edu

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Abstract

This article can be divided into two loosely connected parts. The first part is devoted to proving a singular version of the logarithmic Kodaira–Akizuki–Nakano vanishing theorem of Esnault and Viehweg in the style of Navarro-Aznar et al. This in turn is used to prove other vanishing theorems. In the second part, these vanishing theorems are used to prove an Arakelov–Parshin type boundedness result for families of canonically polarized varieties with rational Gorenstein singularities.


Key Words: families; general type; vanishing theorems; rational singularities.