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I've been told many times that the Torelli map $J:\mathcal{M}_g\to \mathcal{A}_g$ for ($g\geq 2$, and at least on the level of coarse moduli spaces, over $\mathbb{C}$) gives an isomorphism of Picard g …

For the purposes of this question, let the Hodge bundle $\lambda$ be the bundle on a fibration of abelian varieties $X\to B$ with fiber over $b\in B$ the space of 1-forms on $X_b$, or the pullback to …

You need the field extension to have transcendence degree 1 over $\mathbb{C}$ to get a Riemann surface. More generally, you can get an algebraic curve at least for every transcendence degree 1 extens …

For deformation theory and complex manifolds, I'm a fan of Manetti's lecture notes.

I'm teaching a course over the summer (it's a sort of make-your-own course for non-majors) and I'm planning on organizing it as a math history course, hitting on major threads through about 1900, and …

"Algebraic Geometry and Arithmetic Curves" by Liu might be good, it covers a lot of the same material, but does it more arithmetically. There's also "An Invitation to Arithmetic Geometry" by Lorenzin …

You would probably do well with any of the resources under "D-modules" on Gaitsgory's page. Ginzburg's lectures are good, as is the book by Hotta, Takeuchi and Tanisaki.

Is there a good reference for the structure of the Chow ring of $\mathcal{A}_g$, the moduli space of complex principally polarized abelian varieties? More generally, references for the intersection th …

You might want to look up some things about index theorems (particularly Atiyah-Singer). They tend to relate topological and geometric data, so you can put geometric data in and topological data out. …

I was wondering: is there a good place to find exercises in Hodge theory? Mostly computations and proving small (preferably nifty) theorems, is what I have in mind. Something roughly like the Problem …

I have to agree strongly with Ame's answer, in part. Weibel is a great place to go for the formalism. Once you have a little bit of the formalism, though, where to go depends on interests. To reall …

And actually, as a partial answer to my own question, I just stumbled across Schubert's "Kalkul" on Google Books, and it looks complete, which makes me rather happy, though other portions of the quest …

I want to start out by making this clear: I'm NOT looking for the modern proofs and rigorous statements of things. What I am looking for are references for classical enumerative geometry, back before …

You can start with these notes by Vistoli, which talk about that stuff in the direction of doing stacks and descent theory. The other articles in FGA explained might be useful, as they do a lot of mo …

Polya's "How to Solve It" is a good one. When prepping for the Putnam, I used "Problem Solving Through Problems"