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Results tagged with ag.algebraic-geometry
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user 20391
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
9
votes
1
answer
581
views
Is there an $(\infty,2)$-category with morphisms given by $D^b\text{Coh}$?
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 …
- 1,589
3
votes
2
answers
843
views
Fourier--Mukai transforms and adjunction
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 …
- 1,589
39
votes
2
answers
5k
views
Why is there a connection between enumerative geometry and nonlinear waves?
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 …
- 1,589
5
votes
0
answers
500
views
Is there an easy way to write down the singular cohomology of a hypersurface in a toric vari...
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 …
- 1,589
8
votes
1
answer
410
views
How many "elementary" characterizations of twisted SU(2) representation varieties are known?
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 …
- 1,589