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http://dx.doi.org/10.4134/BKMS.b160683

BIRATIONALLY RIGID COMPLETE INTERSECTIONS OF CODIMENSION TWO  

Evans, Daniel (Department of Mathematical Sciences The University of Liverpool)
Pukhlikov, Aleksandr (Department of Mathematical Sciences The University of Liverpool)
Publication Information
Bulletin of the Korean Mathematical Society / v.54, no.5, 2017 , pp. 1627-1654 More about this Journal
Abstract
We prove that in the parameter space of M-dimensional Fano complete intersections of index one and codimension two the locus of varieties that are not birationally superrigid has codimension at least ${\frac{1}{2}}(M-9)(M-10)-1$.
Keywords
Fano complete intersection; maximal singularity; mobile linear system; multiplicity;
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1 W. Fulton, Intersection Theory, Springer-Verlag, 1984.
2 V. A. Iskovskikh and A. V. Pukhlikov, Birational automorphisms of multi-dimensional algebraic varieties, J. Math. Sci. 82 (1996), no. 4, 3528-3613.   DOI
3 J. Kollar et al., Flips and Abundance for Algebraic Threefolds, Asterisque 211 (1993).
4 T. Okada, Birational Mori fiber structures of $\mathbb{Q}$-Fano 3-fold weighted complete intersections. II, ArXiv:1310.5320.
5 T. Okada, Birational Mori ber structures of $\mathbb{Q}$-Fano 3-fold weighted complete intersections. III, ArXiv:1409.1506.
6 T. Okada, Birational Mori fiber structures of $\mathbb{Q}$-Fano 3-fold weighted complete intersections, Proc. Lond. Math. Soc. 109 (2014), no. 6, 1549-1600.   DOI
7 A. V. Pukhlikov, Maximal singularities on the Fano variety $V^3_6$, Moscow Univ. Math. Bull. 44 (1989), no. 2, 70-75.
8 A. V. Pukhlikov, Birational automorphisms of Fano hypersurfaces, Invent. Math. 134 (1998), no. 2, 401-426.   DOI
9 A. V. Pukhlikov, Fiberwise birational correspondences, Math. Notes 68 (2000), no. 1, 103-112.   DOI
10 A. V. Pukhlikov, Birationally rigid Fano complete intersections, J. Reine Angew. Math. 541 (2001), 55-79.
11 A. V. Pukhlikov, Birational geometry of algebraic varieties with a pencil of Fano cyclic covers, Pure Appl. Math. Q. 5 (2009), no. 2, 641-700.   DOI
12 A. V. Pukhlikov, Birationally Rigid Varieties, Mathematical Surveys and Monographs 190, AMS, 2013.
13 V. V. Shokurov, Three-dimensional log flips, Izv. Math. 40 (1993), no. 1, 95-202.   DOI
14 A. V. Pukhlikov, Birationally rigid complete intersections of quadrics and cubics, Izv. Math. 77 (2013), no. 4, 795-845.   DOI
15 A. V. Pukhlikov, Birationally rigid Fano complete intersections. II, J. Reine Angew. Math. 688 (2014), 209-218.
16 F. Suzuki, Birational rigidity of complete intersections, ArXiv:1507.00285.
17 A. V. Pukhlikov, Birationally rigid Fano double hypersurfaces, Sb. Math. 191 (2000), no. 6, 883-908.   DOI
18 I. A. Cheltsov, Nonrationality of a four-dimensional smooth complete intersection of a quadric and a quadric not containing a plane, Sb. Math. 194 (2003), no. 11-12, 1679-1699.   DOI
19 H. Ahmadinezhad and T. Okada, Birationally rigid Pfaffian Fano 3-folds, ArXiv: 1508.02974.
20 F. Call and G. Lyubeznik, A simple proof of Grothendieck's theorem on the parafactoriality of local rings, Commutative algebra: syzygies, multiplicities, and birational algebra (South Hadley, MA, 1992), 15-18, Contemp. Math., 159, Amer. Math. Soc., Providence, RI, 1994.
21 I. A. Cheltsov, Double cubics and double quartics, Math. Z. 253 (2006), no. 1, 75-86.   DOI
22 T. de Fernex, Erratum to: Birationally rigid hypersurfaces, ArXiv: 1506:07086.
23 I. A. Cheltsov and M. M. Grinenko, Birational rigidity is not an open property, Bull. Korean Math. Soc. 54 (2017), no. 5, 1485-1526.   DOI
24 Th. Eckl and A. V. Pukhlikov, On the locus of non-rigid hypersurfaces, In: Automorphisms in birational and ane geometry, 121-139, Springer Proc. Math. Stat., 79, Springer, Cham, 2014.
25 T. de Fernex, Birationally rigid hypersurfaces, Invent. Math. 192 (2013), no. 3, 533-566.   DOI