The Eisenbud-Green-Harris Conjecture

Abstract: The $f$-vector of a simplicial complex is a finite sequence of integers defined by the number of $i$-dimensional faces of the complex. All possible such vectors are completely characterized thanks to a classical theorem by Kruskal and Katona. This result, when rephrased in terms of Hilbert functions of certain quotients of polynomial rings by monomial ideals, extends the celebrated theorem of Macaulay on lexicographic ideals. The Eisenbud-Green-Harris conjecture is a further generalization of both the Kruskal-Katona theorem and the well-known Cayley–Bacharach theorem for plane curves. I will survey the known results on this conjecture including a recent joint work with Alessandro De Stefani.

Mathematics

Audience: advanced learners

IIT Bombay Virtual Commutative Algebra Seminar

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