The Eisenbud-Green-Harris conjecture for fast-growing degree sequences

Let S be a standard graded polynomial ring over a field, and I be a homogeneous ideal that contains a regular sequence of degrees d1, . . . , dn. We prove the Eisenbud-GreenHarris conjecture when the forms of the regular sequence satisfy di > Pi−1 j=1(dj − 1), improving a result obtained in 2008 by the first author and Maclagan. Except for the sporadic case of a regular sequence of five quadrics, due to G¨unt¨urk¨un and Hochster and for which we include a short alternative argument, the results of this paper recover all known cases where only the degrees of the regular sequence are fix