Abstract:
A criterion for the non-singularity of a complete intersection of two fibrewise quadrics in PP1(O(d1)⊕⋯⊕O(d5)) is obtained.
The following addition to Alexeev's theorem on the rationality of standard Del Pezzo fibrations of degree 4 over P1 is deduced as a consequence: each fibration of this kind with
topological Euler characteristic χ(X)=−4 is proved to be rational.
Bibliography: 10 titles.
Citation:
K. A. Shramov, “On the rationality of non-singular threefolds with a pencil of Del Pezzo surfaces of degree 4”, Sb. Math., 197:1 (2006), 127–137
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\by K.~A.~Shramov
\paper On the rationality of non-singular threefolds with a pencil of Del~Pezzo surfaces of degree~4
\jour Sb. Math.
\yr 2006
\vol 197
\issue 1
\pages 127--137
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Linking options:
https://www.mathnet.ru/eng/sm1498
https://doi.org/10.1070/SM2006v197n01ABEH003749
https://www.mathnet.ru/eng/sm/v197/i1/p133
This publication is cited in the following 10 articles:
Yuri Prokhorov, “Rationality of Fano threefolds with terminal Gorenstein singularities, II”, Rend. Circ. Mat. Palermo (2), 72 (2023), 1797–1821
Krylov I. Okada T., “Stable Rationality of Del Pezzo Fibrations of Low Degree Over Projective Spaces”, Int. Math. Res. Notices, 2020:23 (2020), 9075–9119
Krylov I., “Birational Geometry of Del Pezzo Fibrations With Terminal Quotient Singularities”, J. Lond. Math. Soc.-Second Ser., 97:2 (2018), 222–246
Yu. G. Prokhorov, “The rationality problem for conic bundles”, Russian Math. Surveys, 73:3 (2018), 375–456
Ahmadinezhad H., “On pliability of del Pezzo fibrations and Cox rings”, J. Reine Angew. Math., 723 (2017), 101–125
Brendan Hassett, Yuri Tschinkel, “Quartic del Pezzo surfaces over function fields of curves”, centr.eur.j.math, 12:3 (2014), 395
Asher Auel, Marcello Bernardara, Michele Bolognesi, “Fibrations in complete intersections of quadrics, Clifford algebras, derived categories, and rationality problems”, Journal de Mathématiques Pures et Appliquées, 2013
Kaloghiros A.-S., “A Classification of Terminal Quartic 3-Folds and Applications to Rationality Questions”, Math. Ann., 354:1 (2012), 263–296
Cheltsov I, “Nonrational del Pezzo fibrations”, Adv. Geom., 8:3 (2008), 441–450
M. M. Grinenko, “Fibrations into del Pezzo surfaces”, Russian Math. Surveys, 61:2 (2006), 255–300
Citation in format AMSBIB
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