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# Mathematical Research Letters

## Volume 27 (2020)

### Number 5

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

Pages: 1341 – 1365

DOI: https://dx.doi.org/10.4310/MRL.2020.v27.n5.a4

#### Authors

#### Abstract

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