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I do not know very much about quantum field theory, but I have seen, in my reading, that stable graphs can appear in QFT in the form of, I think, Feynman diagrams. By stable graph I mean a "graph with …

I am interested in this claim: The $n$th symmetric power $C^{(n)}$ of a genus $g$ curve $C$ is isomorphic to the projectivization $\mathbb{P}(E_n)$ of the sheaf $E_n := \pi_\ast(P_n)$ over the Jacobi …

I am currently trying to learn a bit about Grothendieck-Riemann-Roch... To try to get a better feeling for it, I am looking for examples of nice applications of GRR applied to a proper morphism $X \t …

From the discussion at Hochschild cohomology and A-infinity deformations, it seems that general Hochschild cohomology classes correspond to deformations where the deformation parameter can have nonzer …

Suppose I tried to take Hartshorne chapter II and re-do all of it with non-commutative rings rather than commutative rings. Is this possible? Which parts work in the non-commutative setting and which …

In his answer to this question, Scott Carnahan mentions "mirror symmetry mod p". What is that? (Some kind of) Gromov-Witten invariants can be defined for varieties over fields other than $\mathbb{C} …

Hi, I'm looking for a reference for the fact that the moduli stack $M_{GL_r,X}$ of $GL_r$-bundles over $X$ is an algebraic (Artin) stack. I'm only interested in the case where $X$ is a curve (for now …

In this question, Ariyan asks about the question of uniqueness of extensions of vector bundles when they exist. Sasha's answer suggests that extensions of vector bundles don't always exist. More pre …

Apparently you can compute the h^{p,q}'s of smooth things in, for example, Macaulay. Here's an example: computing the h^{p,q}'s of a quintic hypersurface in P^4.

Are there any general methods for computing fundamental group or singular cohomology (including the ring structure, hopefully) of a projective variety (over C of course), if given the equations defini …

Let $X$ be a nice variety over $\mathbb{C}$, where nice probably means smooth and proper. I want to know: How can we show that the hypercohomology of the algebraic de Rham complex agrees with the hyp …

I have several naive and possibly stupid questions about deformations of categories. I hope that someone can at least point me to some appropriate references. What is a deformation of a (linear, dg, …

I know that Hilbert schemes can be very singular. But are there any interesting and nontrivial Hilbert schemes that are smooth? Are there any necessary conditions or sufficient conditions for a Hilber …

What are some examples of compact Kaehler manifolds (or smooth complex projective varieties) that are not isomorphic as complex manifolds (or as varieties), but are isomorphic as symplectic manifolds …

Following, e.g., Wikipedia's definitions, the (small) quantum cohomology ring of $X$ is defined over a "Novikov ring" consisting of formal power series of the form $$ \sum_{\beta \in H_2(X;\mathbb{Z}) …