The Eisenbud-Green-Harris Conjecture for Defect Two Quadratic Ideals

2018/12/18 by Gunturkun, Sema, Hochster, Melvin
#13A02 #13A15 #13D40 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1812.07539

Abstract

The Eisenbud-Green-Harris (EGH) conjecture states that a homogeneous ideal in a polynomial ring K[x₁, …, x_n] over a field K that contains a regular sequence f₁, …, f_n with degrees a_i, i=1, …, n has the same Hilbert function as a lex-plus-powers ideal containing the powers x_i^a_i, i=1, …, n. In this paper, we discuss a case of the EGH conjecture for homogeneous ideals generated by n+2 quadrics containing a regular sequence f₁, …, f_n and give a complete proof for EGH when n=5 and a₁=⋯=a₅=2.

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