Mathematical Research Letters

Volume 27 (2020)

Number 5

The Eisenbud–Green–Harris conjecture for defect two quadratic ideals

Pages: 1341 – 1365



Sema Güntürkün (Department of Mathematics and Statistics, Amherst College, Amherst, Massachusetts, U.S.A.)

Melvin Hochster (Department of Mathematics, University of Michigan, Ann Arbor, Mich., U.S.A.)


The Eisenbud–Green–Harris (EGH) conjecture states that a homogeneous ideal in a polynomial ring $K[x_1, \dotsc, x_n]$ over a field $K$ that contains a regular sequence $f_1, \dotsc , f_n$ with degrees $a_i, i =1, \dotsc , n$ has the same Hilbert function as a lex-plus-powers ideal containing the powers $x^{a_i}_i , i = 1, \dotsc , n$. In this paper, we discuss a case of the EGH conjecture for homogeneous ideals generated by $n + 2$ quadrics containing a regular sequence $f_1, \dotsc , f_n$ and give a complete proof for EGH when $n = 5$ and $a_1 = \dotsc = a_5 = 2$.

Received 1 February 2019

Accepted 15 June 2019

Published 12 January 2021