Kuznetsov's Fano threefold conjecture via Hochschild-Serre algebra

Abstract

Let $Y$ be a smooth quartic double solid regarded as a degree 4 hypersurface of the weighted projective space $\mathbb{P}(1,1,1,1,2)$. We study the multiplication of Hochschild-Serre algebra of its Kuznetsov component $\mathcal{K}u(Y)$, via matrix factorization. As an application, we give a new disproof of Kuznetsov's Fano threefold conjecture.

13 pages, add more details in the proof of Theorem 3.1, correct typos, remove the appendix which is not relevant to the main topic. Final version, to appear in Math.Z