Krylov, Igor; Okada, Takuzo Stable rationality of del Pezzo fibrations of low degree over projective spaces. (English) Zbl 1457.14082 Int. Math. Res. Not. 2020, No. 23, 9075-9119 (2020). Summary: The main aim of this article is to show that a very general three-dimensional del Pezzo fibration of degrees 1, 2, and 3 is not stably rational except for a del Pezzo fibration of degree 3 belonging to explicitly described two families. Higher-dimensional generalizations are also discussed and we prove that a very general del Pezzo fibration of degrees 1, 2, and 3 defined over the projective space is not stably rational provided that the anti-canonical divisor is not ample. Cited in 9 Documents MSC: 14J26 Rational and ruled surfaces 14D06 Fibrations, degenerations in algebraic geometry PDFBibTeX XMLCite \textit{I. Krylov} and \textit{T. Okada}, Int. Math. Res. Not. 2020, No. 23, 9075--9119 (2020; Zbl 1457.14082) Full Text: DOI arXiv Link