Frobenius Amplitude, Ultraproducts, and Vanishing on Singular Spaces
Donu Arapura
TL;DR
This paper extends vanishing theorems to singular complex projective varieties by generalizing the Deligne-Illusie decomposition and introduces a new ultraproduct-based definition of Frobenius amplitude.
Contribution
It provides a Kodaira type vanishing theorem for singular spaces and offers a novel ultraproduct approach to Frobenius amplitude.
Findings
Proved a vanishing theorem for singular varieties.
Extended Deligne-Illusie decomposition to the Du Bois complex.
Introduced a new ultraproduct-based definition of Frobenius amplitude.
Abstract
When X is a singular complex projective variety, we prove a Kodaira type vanishing theorem generalizing results of Navarro Aznar and others. This is proved by extending the Deligne-Illusie decomposition to the Du Bois complex. We also give a new definition of Frobenius amplitude (introduced in math.AG/0202129) using ultraproducts.
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