Logarithmic Kodaira-Akizuki-Nakano vanishing and Arakelov-Parshin boundedness for singular varieties

Details Logarithmic Kodaira-Akizuki-Nakano vanishing and Arakelov-Parshin boundedness for singular varieties Logarithmic Kodaira-Akizuki-Nakano vanishing and Arakelov-Parshin boundedness for singular varieties

2000-03-03

arxiv.org/abs/math/0003019v4

Mathematics

Algebraic Geometry

23 pages, typos/errors corrected, definition of strong ampleness is made more general more typos/errors corrected, 6.4 made sl

Scientific paper

The article has two parts. The first part is devoted to proving a singular version of the logarithmic Kodaira-Akizuki-Nakano vanishing theorem of Esnault and Viehweg. This is then 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.

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