Stable Rationality of del Pezzo Fibrations of Low Degree Over Projective Spaces

DOI10.1093/IMRN/RNY252zbMATH Open1457.14082arXiv1701.08372OpenAlexW2963279606WikidataQ129166071 ScholiaQ129166071MaRDI QIDQ5854245

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Publication date: 16 March 2021

Published in: (Search for Journal in Brave)

Abstract: The main aim of this article is to show that a very general 3-dimensional del Pezzo fibration of degree 1,2,3 is not stably rational except for a del Pezzo fibration of degree 3 belonging to explicitly described 2 families. Higher dimensional generalizations are also discussed and we prove that a very general del Pezzo fibration of degree 1,2,3 defined over the projective space is not stably rational provided that the anticanonical divisor is not ample.

Full work available at URL: https://arxiv.org/abs/1701.08372

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