Geodesic
Singularities of Algebraic Subvarieties and Problems of Birational Geometry
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Singularities and applications, Tome 267 (2009), pp. 245-257.

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We consider the connection between the problem of estimating the multiplicity of an algebraic subvariety at a given singular point and the problem of describing birational maps of rationally connected varieties. We describe the method of hypertangent divisors which makes it possible to give bounds for the multiplicities of singular points. The concept of birational rigidity of algebraic varieties is discussed. 
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A. V. Pukhlikov. Singularities of Algebraic Subvarieties and Problems of Birational Geometry. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Singularities and applications, Tome 267 (2009), pp. 245-257. http://geodesic.mathdoc.fr/item/TM_2009_267_a18/

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