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Register a new userThe lower bound on the HK multiplicities of quadric hypersurfaces
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Vijaylaxmi Trivedi
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Here we prove that the Hilbert-Kunz mulitiplicity of a quadric hypersurface of dimension $d$ and odd characteristic $pgeq 2d-4$ is bounded below by $1+m_d$, where $m_d$ is the $d^{th}$ coefficient in the expansion of $mbox{sec}+mbox{tan}$. This proves a part of the long standing conjecture of Watanabe-Yoshida. We also give an upper bound on the HK multiplicity of such a hypersurface. We approach the question using the HK density function and the classification of ACM bundles on the smooth quadrics via matrix factorizations.
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