Geodesic
Existence of the Kähler–Einstein Metric on Certain Fano Complete Intersections
Matematičeskie zametki, Tome 88 (2010) no. 4, pp. 575-582 Cet article a éte moissonné depuis la source Math-Net.Ru

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For certain families of Fano complete intersections we prove an estimate from below for the global (log) canonical threshold, which implies the existence of Kähler–Einstein metric on generic varieties in these families.
Mots-clés : Kähler–Einstein metric, birational morphism.
Keywords: Fano variety, projective space, complete intersection, global canonical threshold, $\log$ canonical threshold, effective divisor 
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A. V. Pukhlikov. Existence of the Kähler–Einstein Metric on Certain Fano Complete Intersections. Matematičeskie zametki, Tome 88 (2010) no. 4, pp. 575-582. http://geodesic.mathdoc.fr/item/MZM_2010_88_4_a8/

[1] A. V. Pukhlikov, “Birational geometry of algebraic varieties with a pencil of Fano complete intersections”, Manuscripta Math., 121:4 (2006), 491–526 | DOI | MR | Zbl

[2] J.-P. Demailly, J. Kollár, “Semi-continuity of complex singularity exponents and Kähler–Einstein metrics on Fano orbifolds”, Ann. Sci. École Norm. Sup. (4), 34:4 (2001), 525–556 | MR | Zbl

[3] A. M. Nadel, “Multiplier ideal sheaves and Kähler–Einstein metrics of positive scalar curvature”, Ann. of Math. (2), 132:3 (1990), 549–596 | DOI | MR | Zbl

[4] G. Tian, “On Kähler–Einstein metrics on certain Kähler manifolds with $C_1(M)>0$”, Invent. Math., 89:2 (1987), 225–246 | DOI | MR | Zbl

[5] A. V. Pukhlikov, “Birational automorphisms of Fano hypersurfaces”, Invent. Math., 134:2 (1998), 401–426 | DOI | MR | Zbl

[6] A. V. Pukhlikov, “Birationally rigid Fano complete intersections”, J. Reine Angew. Math., 541 (2001), 55–79 | DOI | MR | Zbl

[7] A. V. Pukhlikov, “Biratsionalnaya geometriya pryamykh proizvedenii Fano”, Izv. RAN. Ser. matem., 69:6 (2005), 153–186 | MR | Zbl

[8] I. A. Cheltsov, K. A. Shramov, “Log-kanonicheskie porogi neosobykh trekhmernykh mnogoobrazii Fano”, UMN, 63:5 (2008), 73–180 | MR | Zbl

[9] A. V. Pukhlikov, “Biratsionalno zhestkie iterirovannye dvoinye nakrytiya Fano”, Izv. RAN. Ser. matem., 67:3 (2003), 139–182 | MR | Zbl