3 problems

D-orbifold string theory conjecture. There is an inner local system $\mathcal L$ such that the ordinary cohomology of $Y$ is the direct sum of $H^*_{orb}(X,\mathcal L)$ and the coh…

Let $X$ be a Calabi–Yau Gorenstein orbifold, and let a desingularization of $X$ be given. An inner local system is a compatible assignment of a flat orbifold line bundle to each se…

Smoothness conjecture. In Cases 1–4, the invariant Hilbert scheme $\mathcal{H}$ is smooth if and only if $\nu$ is flat or the data belong to one of the cases listed in the main the…