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Results tagged with ag.algebraic-geometry
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user 6776
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
1
vote
How to compute div(dx)
When I saw that example in Silverman for the first, it didn't understand much out of it either. I'm still not good at it, but I'm trying to solve it using theorems and examples in Silverman. However, …
- 601
1
vote
1
answer
343
views
Proof of "generic curve of genus at least 2 has no nontrivial maps to a positive genus curve"
I searched for it for a long time, but it seems that everybody is taking this for granted and does not bother to point out a proof. Would it be possible that someone points me to a proof or makes me s …
- 601
0
votes
1
answer
338
views
Reference for notation $H^0(C, mK)$
I am reading the draft of "Equations of Riemann Surfaces of Genus 4, 5 and 6 wih Large Automorphism groups" and the author starts using the notation $H^0(C, mK)$ on page 3, without explaining it. As t …
- 601
0
votes
1
answer
342
views
Necessary/Sufficient condition/Algorithm that tells me a function field is a kummer extension
I start my question with an example. Suppose $F/K$ be the function field generated by $x^n - yx^{n-1} - 1 = 0$. It is not a cyclic over K(y), but if I set $t = yx^{n-1}$ then we have $K(x,t) \subset K …
- 601
1
vote
0
answers
204
views
Which rational subfields are corresponding to the two dimensional subspaces of holomorphic d...
I implemented the algorithm that Felipe Voloch's suggested in his reply to the question:
Subfields of a function field
the algorithm is here:
Subfields of a function field
I considered the functio …
- 601
14
votes
2
answers
1k
views
Subfields of a function field
Is there an algorithm for generating (some or all) subfields of a certain genus of a given function field (even a random one,I mean for example generating a random elliptic subfield of a certain given …
- 601