10 problems

Let $X$ be a complex manifold of dimension $d$, and let ${\cal M}^\bullet$ be a complex of ${\cal D}_X$-modules with bounded good cohomology. Choose a filtration compatible with th…

Let $M$ be a smooth projective variety, let $\pi$ be a group, and let $f:M\to B\pi$ be a continuous map. For $\alpha\in H^*(B\pi;\mathbb{Q})$, let $\operatorname{Td}(M)$ denote the…

Let $X$ be a complex manifold of dimension $d$, let ${\cal M}^\bullet$ be an object of $\operatorname{D}^b_{good}({\cal D}^{op}_X)$, and let $\Lambda$ be a conic subvariety of…

Debarre–Huybrechts–Macrì–Voisin conjecture. Then $c_X=(2n-1)!!$ and the Huybrechts–Riemann–Roch polynomial of $X$ is

Relative tropical Riemann–Roch conjecture.

Moderate-position tropical Riemann–Roch conjecture. If $D$ is in moderate position on $X$, then

Suppose that $f\colon X\to Y$ is a morphism equipped with an almost perfect obstruction theory with virtual tangent class $[T_{X/Y}]-[\mathcal{O}b_X]\in K_0(X)$. Assume that this c…

Numerical Riemann–Roch conjecture. The Huybrechts–Riemann–Roch polynomial of $X$ satisfies

Let $\Delta$ be a tropical surface, let $D$ be a Cartier divisor on $\Delta$, and let $K_\Delta$ be the divisor obtained by summing $(\operatorname{deg} r-2)[r]$ over the ridges…

Let $\pi\colon E\to B$ be an oriented surface bundle with closed fibers of genus $g$, equipped with a fiberwise metric. Let $\mathcal{H}(E)$ be the associated Hodge bundle, with fi…