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arXiv · 2607.20035

Quadratic Ideals in Six Variables and the Eisenbud--Green--Harris Conjecture

Abed Abedelfatah
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Abstract

In this paper, we study the Eisenbud--Green--Harris (EGH) conjecture for ideals generated by quadrics. We establish a sharp lower bound for the dimension of the cubic component of an ideal generated by a regular sequence of six quadrics and two additional quadrics in six variables. Furthermore, we prove the Eisenbud--Green--Harris conjecture for almost complete intersections of quadrics in six variables.

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Abed Abedelfatah. 2026-07-22. Quadratic Ideals in Six Variables and the Eisenbud--Green--Harris Conjecture. https://arxiv.org/abs/2607.20035

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