On the Eisenbud-Green-Harris conjecture.

Abstract: A generalization of the Macaulay’s theorem on the growth of Hilbert functions of homogeneous ideals in $K[x_1,\ldots, x_n]$ is conjectured by Eisenbud, Green and Harris in the 90s. The conjecture, also known as the EGH conjecture, states that the lex-plus-powers ideals show an extremal behavior among the homogeneous ideals containing regular sequences in terms of their Hilbert functions. In this talk, our focus will be on a case of the EGH conjecture for the homogeneous ideals containing a regular sequence of quadratic forms. This is a joint work with Mel Hochster.

commutative algebraalgebraic geometrynumber theoryrepresentation theory

Audience: advanced learners

UCGEN - Uluslararası Cebirsel GEometri Neşesi

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