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Results tagged with ag.algebraic-geometry
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user 1703
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
7
votes
Examples in mirror symmetry that can be understood.
I'm not sure if this is what you're looking for, but the paper "Mirror symmetry and Elliptic curves" by R. Dijkgraaf might be provide a good example.
The example in that paper concerns the mirror of …
- 6,242
3
votes
Accepted
Enumerativity of Gromov-Witten invariants of orbifolds
One simple example (although it is a genus 0 example) is the following.
Consider a global quotient $\mathscr{X} = [X/(\mathbb{Z}/2)]$. Then if we look at the genus 0 GW theory of $\mathscr{X}$ where …
- 6,242
8
votes
1
answer
727
views
To what extent does Poincare duality hold on moduli stacks?
Poincare duality gives us, for a smooth orientable $n$-manifold, an isomorphism $H^k(M) \to H_{n-k}(M)$ given by $\gamma \mapsto \gamma \frown [M]$ where $[M]$ is the fundamental class of the manifold …
- 6,242
14
votes
0
answers
502
views
Am I missing something about this notion of Mirror Symmetry for abelian varieties?
This is a continuation of my recent question: Mirror symmetry for polarized abelian surfaces and Shioda-Inose K3s.
In the comments of the question, I was directed to the paper http://arxiv.org/abs/he …
- 6,242
12
votes
2
answers
1k
views
What classes am I missing in the Picard lattice of a Kummer K3 surface?
Constructing the Kummer K3 of an Abelian surface $A$, we have an obvious 22-dimensional collection of classes in $H^2(K3, \mathbb{Z})$ given by the 16 (-2)-curves (which by construction do not interse …
- 6,242
6
votes
What is a branched Riemann surface with cuts?
Since no one has answered the genus computation, here goes:
The Riemann-Hurwitz formula states that for a map of Riemann surfaces $f : C_1 \to C_2$, that we have
$$
\chi(C_1) = n\chi(C_2) - \deg R
$ …
- 6,242
7
votes
2
answers
2k
views
What is a good reference (preferably thorough) for the Derived Category of a scheme/orbifold...
I've sort of circled around the idea of derived categories a few times, read a few introductory papers ("Derived Categories for the working mathematician", e.g.), and feel now that this is something t …
- 6,242