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 P(1,1,1,1,2). We study the multiplication of the Hochschild-Serre algebra of its Kuznetsov component Ku(Y) via matrix factorization. As an application, we give a new disproof of Kuznetsov's Fano threefold conjecture.