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Mat. Sb., 2006, Volume 197, Number 1, Pages 133–144 (Mi msb1498)  

This article is cited in 8 scientific papers (total in 8 papers)

On the rationality of non-singular threefolds with a pencil of Del Pezzo surfaces of degree 4

K. A. Shramov

M. V. Lomonosov Moscow State University

Abstract: A criterion for the non-singularity of a complete intersection of two fibrewise quadrics in $\mathbb P_{\mathbb P^1}(\mathscr O(d_1)\oplus…\oplus\mathscr O(d_5))$ is obtained. The following addition to Alexeev's theorem on the rationality of standard Del Pezzo fibrations of degree 4 over $\mathbb P^1$ is deduced as a consequence: each fibration of this kind with topological Euler characteristic $\chi(X)=-4$ is proved to be rational.
Bibliography: 10 titles.

DOI: https://doi.org/10.4213/sm1498

Full text: PDF file (458 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2006, 197:1, 127–137

Bibliographic databases:

Document Type: Article
UDC: 512.76
MSC: 14J30, 14E08
Received: 08.02.2005

Citation: K. A. Shramov, “On the rationality of non-singular threefolds with a pencil of Del Pezzo surfaces of degree 4”, Mat. Sb., 197:1 (2006), 133–144; Sb. Math., 197:1 (2006), 127–137

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. M. Grinenko, “Fibrations into del Pezzo surfaces”, Russian Math. Surveys, 61:2 (2006), 255–300  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. Cheltsov I, “Nonrational del Pezzo fibrations”, Adv. Geom., 8:3 (2008), 441–450  crossref  mathscinet  zmath  isi  scopus
    3. Kaloghiros A.-S., “A Classification of Terminal Quartic 3-Folds and Applications to Rationality Questions”, Math. Ann., 354:1 (2012), 263–296  crossref  mathscinet  zmath  isi  elib  scopus
    4. 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  crossref  mathscinet  scopus
    5. Brendan Hassett, Yuri Tschinkel, “Quartic del Pezzo surfaces over function fields of curves”, centr.eur.j.math, 12:3 (2014), 395  crossref  mathscinet  zmath  isi  scopus
    6. Ahmadinezhad H., “On pliability of del Pezzo fibrations and Cox rings”, J. Reine Angew. Math., 723 (2017), 101–125  crossref  mathscinet  zmath  isi
    7. Krylov I., “Birational Geometry of Del Pezzo Fibrations With Terminal Quotient Singularities”, J. Lond. Math. Soc.-Second Ser., 97:2 (2018), 222–246  crossref  mathscinet  zmath  isi  scopus
    8. Yu. G. Prokhorov, “The rationality problem for conic bundles”, Russian Math. Surveys, 73:3 (2018), 375–456  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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