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Recently I encountered in a class the fact that there is a generating function of Gromov–Witten invariants that satisfies the Korteweg–de Vries hierarchy. Let me state the fact more precisely. Defin …

My question is: Has anyone constructed an $(\infty,2)$-category whose objects are (projective, maybe smooth, ...) varieties, and where the 1-morphisms from $X$ to $Y$ are given by $D^b_\infty\text …

If $X$ and $Y$ are smooth projective varieties, $p: X \times Y \to X$ and $q: X \times Y \to Y$ are the projections, and $\mathcal{P}$ is an object in $D^b(X \times Y)$, then the Fourier--Mukai transf …

Recently I had to compute the rational singular cohomology ring of a hypersurface in a product of projective spaces. I managed to do it, but only by interpreting this variety as a blowup of projectiv …

If $\Sigma_g$ is a genus-$g$ surface, $g \geq 2$, then let $\mathcal{M}(\Sigma_g)$ be its twisted SU(2) representation variety, i.e. $$\mathcal{M}(\Sigma_g) := \{ (A_1, B_1, \ldots, A_g, B_g) \in SU(2 …