7 problems

Let $X$ be a numerical $(K3)^{[2]}$ and suppose that Items (1) through (6) of Proposition (hodgeprop) hold. O'Grady's conditional theorem. Item (1) of Theorem (mainthm1) holds. The…

A Type B $4$-fold is an irreducible symplectic $4$-fold numerically equivalent to $(K3)^{[2]}$ that is birational to a hypersurface of degree at most $12$. O'Grady's nonexistence c…

Let $\mathcal M_4^{(1)}$ be the moduli space under consideration, let $\mathcal M_{\mathrm{Coble4}}^\circ$ be the open locus obtained from smooth stable Coble type quartics, and le…

Let $Sigma^\circ\subset |\mathcal O_{\mathbb P^9}(4)|$ be the locus of Coble type quartics singular exactly along a smooth hyperkähler fourfold in $\mathcal M_4^{(1)}$, and let…

Let $Sigma^\circ\subset |\mathcal O_{\mathbb P^9}(4)|$ be the locus of Coble type quartics singular exactly along a smooth hyperkähler fourfold in $\mathcal M_4^{(1)}$, and let…

Let $d4a4_2$, $d4a4_6$, $d4a4_8$, and $d4a4_d$ for $de5 16$ denote the indicated Heegner divisors, and call a Heegner divisor HLS if it has the HLS property used in the paper. HLS…

Integral transcendental-lattice isometry conjecture. This isometry should hold with integer coefficients: