The ideal containment problem and vanishing loci of homogeneous polynomials

Abstract: We shall discuss Chudnovsky’s and Demailly’s conjectures which provide lower bounds for the answer to the following fundamental question: given a set of points in projective space and a positive integer m, what is the least degree of a homogeneous polynomial vanishing at these points of order at least $m$? Particularly, we shall present the main ideas of the proofs of these conjectures for sufficiently many general points.

Mathematics

Audience: advanced learners

IIT Bombay Virtual Commutative Algebra Seminar

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