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 Izv. RAN. Ser. Mat., 2006, Volume 70, Issue 3, Pages 185–221 (Mi izv580)

Local inequalities and birational superrigidity of Fano varieties

I. A. Cheltsov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We obtain local inequalities for log canonical thresholds and multiplicities of movable log pairs. We prove the non-rationality and birational superrigidity of the following Fano varieties: a double covering of a smooth cubic hypersurface in $\mathbb P^n$ branched over a nodal divisor that is cut out by a hypersurface of degree $2(n-3)\ge 10$; a cyclic triple covering of a smooth quadric hypersurface in $\mathbb P^{2r+2}$ branched over a nodal divisor that is cut out by a hypersurface of degree $r\ge 3$; a double covering of a smooth complete intersection of two quadric hypersurfaces in $\mathbb P^n$ branched over a smooth divisor that is cut out by a hypersurface of degree $n-4\ge 6$.

DOI: https://doi.org/10.4213/im580

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English version:
Izvestiya: Mathematics, 2006, 70:3, 605–639

Bibliographic databases:

UDC: 512.76
MSC: 14E05, 14E07, 14E08, 14J40, 14J45

Citation: I. A. Cheltsov, “Local inequalities and birational superrigidity of Fano varieties”, Izv. RAN. Ser. Mat., 70:3 (2006), 185–221; Izv. Math., 70:3 (2006), 605–639

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/izv580
• https://doi.org/10.4213/im580
• http://mi.mathnet.ru/eng/izv/v70/i3/p185

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. A. V. Pukhlikov, “Birational geometry of Fano double spaces of index two”, Izv. Math., 74:5 (2010), 925–991
2. A. V. Pukhlikov, “Birationally rigid varieties. II. Fano fibre spaces”, Russian Math. Surveys, 65:6 (2010), 1083–1171
3. A. V. Pukhlikov, “Birational geometry of higher-dimensional Fano varieties”, Proc. Steklov Inst. Math., 288, suppl. 2 (2015), S1–S150
4. Pukhlikov A.V., “Birational geometry of Fano hypersurfaces of index two”, Math. Ann., 366:1-2 (2016), 721–782
5. Pukhlikov V A., “Birational Geometry of Singular Fano Hypersurfaces of Index Two”, Manuscr. Math., 161:1-2 (2020), 161–203
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