\BOOKMARK [1][-]{section*.1}{Introduction}{}% 1
\BOOKMARK [1][-]{section.1}{1. Cremona transformation with singular base locus}{}% 2
\BOOKMARK [2][-]{subsection.1.1}{1.1. Terminology and notation}{section.1}% 3
\BOOKMARK [2][-]{subsection.1.2}{1.2. Computing the intersection numbers}{section.1}% 4
\BOOKMARK [1][-]{section.2}{2. Construction of our example}{}% 5
\BOOKMARK [2][-]{subsection.2.1}{2.1. Orthogonal Grassmannian}{section.2}% 6
\BOOKMARK [2][-]{subsection.2.2}{2.2. An explicit example}{section.2}% 7
\BOOKMARK [2][-]{subsection.2.3}{2.3. Proof of Theorem 2.1}{section.2}% 8
\BOOKMARK [2][-]{subsection.2.4}{2.4. Some geometry of the construction}{section.2}% 9
\BOOKMARK [1][-]{section.3}{3. Derived equivalences of K3 surfaces}{}% 10
\BOOKMARK [2][-]{subsection.3.1}{3.1. Derived equivalences and general strategy}{section.3}% 11
\BOOKMARK [2][-]{subsection.3.2}{3.2. The middle cohomology of X}{section.3}% 12
\BOOKMARK [2][-]{subsection.3.3}{3.3. The discriminant groups}{section.3}% 13
\BOOKMARK [2][-]{subsection.3.4}{3.4. Proofs of Theorem 3.1 and its Corollary}{section.3}% 14
\BOOKMARK [2][-]{subsection.3.5}{3.5. Connections between our construction and other approaches}{section.3}% 15
\BOOKMARK [1][-]{section.4}{4. Zero divisors in the Grothendieck ring}{}% 16
\BOOKMARK [1][-]{section.5}{5. Exclusion of alternative constructions}{}% 17
\BOOKMARK [2][-]{subsection.5.1}{5.1. Extracting Diophantine equations}{section.5}% 18
\BOOKMARK [2][-]{subsection.5.2}{5.2. Enumeration of combinatorial cases}{section.5}% 19
\BOOKMARK [2][-]{subsection.5.3}{5.3. Exclusion of cases}{section.5}% 20
\BOOKMARK [2][-]{subsection.5.4}{5.4. Geometric analysis of the remaining case}{section.5}% 21
\BOOKMARK [1][-]{section*.3}{References}{}% 22