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Results tagged with ag.algebraic-geometry
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user 11286
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
5
votes
2
answers
1k
views
Generalize the Proj construction?
I'm wondering if there is a generalization of the Proj construction used in algebraic geometry. Given a graded ring R, which is a monoid homomorphism $R\to \mathbb{N}$, we can form the scheme Proj(R), …
- 3,806
9
votes
1
answer
722
views
Use of Hilbert Schemes in Arithmetic?
I'm curious about the following: What are some arithmetic application of the Hilbert Schemes?
The application of Hilbert schemes in algebraic geometry seems to be a great success, from birational geo …
- 3,806
2
votes
0
answers
106
views
What does the term "3-fold vertex" mean in enumerative geometry?
I read about enumerative geometry recently, namely something about the Gromov-Witten, Donaldson-Thomas and Pandharipande-Thomas invariants, and I was trying to see the picture.
It seems like the term …
- 3,806
20
votes
2
answers
3k
views
Can Chern class/character be categorified?
The Chern character sends the class of a locally free sheaf to the cohomology ring of the underlying variety X. And it is a ring homomorphism from K to H^*. I saw people write its source as the bounde …
- 3,806
10
votes
3
answers
2k
views
Families of ideal sheaves: What's the correct definition?
I'm looking at Bridgeland's paper "Flops and Derived categories" and I got confused on what he meant by a family of ideal sheaves.
Let $Y$ be a scheme, and let $S$ be another scheme. A family of sheav …
- 3,806
13
votes
2
answers
2k
views
Are non-algebraic stacks useful in algebraic geometry?
The title is a bit vague. What I want to know is if there is any geometric application of non-algebraic stacks. I know e.g. the category of coherent sheaves is an example. But I want to ask if people …
- 3,806
15
votes
2
answers
2k
views
How to compute the Picard rank of a K3 surface?
I'm curious about the following question:
Given a K3 surface, how does one proceed to compute its rank?
Of course the answer may depend on the form of the input, i.e. how the K3 is "given". So
…
- 3,806
7
votes
Interpreting $f^*f_*$
To me, pushforword is like taking sections along the fibers, and higher pushforwards are like cohomologies along the fiber.
Think about that $f^*f_*F\to F$ being surjective as globally generated alon …
- 3,806