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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

9 votes
1 answer
5k views

Is a fibration in algebraic geometry a fibre bundle?

Let $X \to B$ be a smooth, proper, dominant map of schemes over $\text{Spec }k$ an algebraically closed field of characteristic zero with $B$ integral. We have the generic fibre $\overline{F}$ defined …
Arnav Tripathy's user avatar
5 votes

Rational map to a non-uniruled manifold

I think you have already answered this yourself, for the most part. We have a birational morphism $X' \to X$ with some exceptional locus $E$ inside $X'$, which is some finite union of ruled components …
Arnav Tripathy's user avatar
24 votes

Survey article on Intersection Theory

Eisenbud and Harris are coming out with a book on intersection theory, "3264 and all that", and if you know Harris's style at all, you'll know it's chock full of down-to-earth examples that should be …
Arnav Tripathy's user avatar
7 votes
0 answers
396 views

Integrality of the mirror map -- non-GKZ examples? Counterexamples?

The mirror map in mirror symmetry is the change-of-variables between the natural coordinatizations on the two mirror sides and is typically a highly-complicated transcendental function (indeed, should …
Arnav Tripathy's user avatar