A. V. Pukhlikov, “Birationally rigid Fano fibre spaces. II”, Izv. Math., 79:4 (2015), 809

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Izvestiya: Mathematics, 2015, Volume 79, Issue 4, Pages 809–837
DOI: https://doi.org/10.1070/IM2015v079n04ABEH002762 (Mi im8273)

This article is cited in 18 scientific papers (total in 18 papers)

Birationally rigid Fano fibre spaces. II

A. V. Pukhlikov

University of Liverpool

English version PDF (427 kB) Citations (18) Russian version article

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DOI: https://doi.org/10.1070/IM2015v079n04ABEH002762

Abstract: We prove the birational rigidity of large classes of Fano–Mori fibre spaces over a base of arbitrary dimension bounded above by a constant that depends only on the dimension of the fibres. To do this, we first show that if every fibre of a Fano–Mori fibre space satisfies certain natural conditions, then every birational map onto another such space is fibrewise. Then we construct large classes of fibre spaces (whose fibres are either Fano double spaces of index 1 or Fano hypersurfaces of index 1) satisfying these conditions.

Keywords: Fano–Mori fibre space, birational rigidity, maximal singularity, hypertangent divisor, log canonical singularity, linear system, canonical class.

Received: 02.07.2014

Bibliographic databases:

Document Type: Article

UDC: 512.7

MSC: 14E05, 14J45, 14D06, 14M22, 14E30

Language: English

Original paper language: Russian

Citation: A. V. Pukhlikov, “Birationally rigid Fano fibre spaces. II”, Izv. Math., 79:4 (2015), 809–837

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/im8273

https://doi.org/10.1070/IM2015v079n04ABEH002762

https://www.mathnet.ru/eng/im/v79/i4/p175

Cycle of papers

Birationally rigid Fano fibrations
A. V. Pukhlikov
Izv. RAN. Ser. Mat., 2000, 64:3, 131–150
Birationally rigid Fano fibre spaces. II
A. V. Pukhlikov
Izv. RAN. Ser. Mat., 2015, 79:4, 175–204

This publication is cited in the following 18 articles:

Jheng-Jie CHEN, “Accumulation points on 3-fold canonical thresholds”, J. Math. Soc. Japan, -1:-1 (2025)
A. V. Pukhlikov, “Birationally rigid hypersurfaces with quadratic singularities of low rank”, Sb. Math., 215:6 (2024), 823–840
Aleksandr Pukhlikov, “Birationally rigid Fano-Mori fibre spaces”, Forum of Mathematics, Sigma, 12 (2024)
de Fernex T., “Birational Rigidity and K-Stability of Fano Hypersurfaces With Ordinary Double Points”, Rend. Circ. Mat. Palermo, 2022
A. V. Pukhlikov, “Birational geometry of varieties fibred into complete intersections of codimension two”, Izv. Math., 86:2 (2022), 334–411
A. V. Pukhlikov, “Effective results in the theory of birational rigidity”, Russian Math. Surveys, 77:2 (2022), 301–354
Pukhlikov V A., “Canonical and Log Canonical Thresholds of Multiple Projective Spaces”, Eur. J. Math., 7:1 (2021), 135–162
Kim I.-K. Okada T. Won J., “Alpha Invariants of Birationally Bi-Rigid Fano 3-Folds i”, Eur. J. Math., 7:1 (2021), 272–308
A. V. Pukhlikov, “Birational geometry of singular Fano double spaces of index two”, Sb. Math., 212:4 (2021), 551–566
A. V. Pukhlikov, “Remarks on Galois Rational Coverings”, Math. Notes, 110:2 (2021), 242–247
A. V. Pukhlikov, “Birational geometry of singular fano hypersurfaces of index two”, Manuscr. Math., 161:1-2 (2020), 161–203
A. V. Pukhlikov, “Rationally connected rational double covers of primitive fano varieties”, Epijournal Geom. Algebr., 4 (2020), 18
C. Fontanari, D. Martinelli, “A remark on rationally connected varieties and mori dream spaces”, Proc. Edinb. Math. Soc., 62:1 (2019), 259–263
D. Evans, A. V. Pukhlikov, “Birationally rigid complete intersections of high codimension”, Izv. Math., 83:4 (2019), 743–769
A. V. Pukhlikov, “Birationally Rigid Finite Covers of the Projective Space”, Proc. Steklov Inst. Math., 307 (2019), 232–244
Thomas Eckl, Aleksandr Pukhlikov, “Effective Birational Rigidity of Fano Double Hypersurfaces”, Arnold Math J., 4:3-4 (2018), 505
A. V. Pukhlikov, “Birational geometry of algebraic varieties fibred into Fano double spaces”, Izv. Math., 81:3 (2017), 618–644
E. Johnstone, “Birationally Rigid Singular Double Quadrics and Double Cubics”, Math. Notes, 102:4 (2017), 508–515

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	569
Russian version PDF:	181
English version PDF:	29
References:	65
First page:	10

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