A modular equality for m$m$‐ovoids of elliptic quadrics

Abstract An ‐ovoid of a finite polar space is a set of points such that every maximal subspace of contains exactly points of . In the case when is an elliptic quadric of rank in , we prove that an ‐ovoid exists only if satisfies a certain modular equality, which depends on and . This condition rules out many of the possible values of . Previously, only a lower bound on was known, which we slightly improve as a byproduct of our method. We also obtain a characterization of the ‐ovoids of for and .