Differential forms on log canonical spaces
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Publication:691693
DOI10.1007/S10240-011-0036-0zbMATH Open1258.14021arXiv1003.2913OpenAlexW2039030220WikidataQ60355700 ScholiaQ60355700MaRDI QIDQ691693
Author name not available (Why is that?)
Publication date: 3 December 2012
Published in: (Search for Journal in Brave)
Abstract: The present paper is concerned with differential forms on log canonical varieties. It is shown that any p-form defined on the smooth locus of a variety with canonical or klt singularities extends regularly to any resolution of singularities. In fact, a much more general theorem for log canonical pairs is established. The proof relies on vanishing theorems for log canonical varieties and on methods of the minimal model program. In addition, a theory of differential forms on dlt pairs is developed. It is shown that many of the fundamental theorems and techniques known for sheaves of logarithmic differentials on smooth varieties also hold in the dlt setting. Immediate applications include the existence of a pull-back map for reflexive differentials, generalisations of Bogomolov-Sommese type vanishing results, and a positive answer to the Lipman-Zariski conjecture for klt spaces.
Full work available at URL: https://arxiv.org/abs/1003.2913
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