Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with ag.algebraic-geometry
Search options not deleted
user 25510
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
2
votes
Questions about some parallel between polynomial and differential equation
The answer to Q2 is provided by Differential algebra
created by Joseph Fels Ritt. He studied differential-algebraic varieties by analogy with algebraic ones.
See Ritt, Joseph Fels, Differential algebr …
- 91.8k
37
votes
Accepted
How did Riemann prove that the moduli space of compact Riemann surfaces of genus $g>1$ has d...
Riemann combines what is called Riemann-Roch and Riemann-Hurwitz nowadays.
He considers the dimension of the space of holomorphic maps of degree $d$ from the Riemann surface of genus $g$ to the sphere …
- 91.8k
14
votes
4
answers
2k
views
Examples of plane algebraic curves
There are many interesting sequences of polynomials which contain
polynomials of arbitrarily high degree, for example classical
orthogonal polynomials. Most of them arise as characteristic polynomials …
- 1,446
3
votes
Quadrature of the Lune
This is indeed the theorem of Chebotarev and
Dorodnov, the original
articles are
Tschebotaröw, Nikolaj
Über quadrierbare Kreisbogenzweiecke. I. (German) Zbl 0010.00103.
Math. Z. 39, 161-175 (1934).
A. …
- 91.8k
1
vote
Calculation of solid angle for rectangle in 6DOF
You can do this without integration, by performing the following steps.
Calculate the coordinates of the vertices of your rectangle. Let the vertices be $v_1,v_2,v_3,v_4$.
Let your point "source" be …
- 91.8k
29
votes
Algebraic geometry over the complex numbers, and beyond
Algebraic geometry began over the field of reals. What Apollonius of Perga did would be certainly qualified today as algebraic geometry: he classified real plane curves of second order and studied the …
- 91.8k
1
vote
Approaching the Riemann-Roch Theorem for algebraic curves
Several proofs are available.
If you are interested in a short algebraic proof, I can recommend S. Lang, Introduction to algebraic and Abelian functions, Addison-Wesley, Reading, MA, 1972. First 25 pa …
- 91.8k
3
votes
Explicit universal covering map for higher genus algebraic curves
The answer is no, except some very special cases. There is a comprehensive book dedicated to this: H. P. de Sain-Gervais, Uniformisation des surfaces de Riemann, ENS Ed., 2010. There is an English tra …
- 91.8k
7
votes
Accepted
Constructing proper holomorphic self-mappings of the unit disk with a given set of branch po...
This (existence and uniqueness) is proved in the paper in much more general setting (in fact, the result is due to E. Picard):
M. Heins, ‘On a class of conformal metrics’, Nagoya Math. J. 21 (1962) 1– …
- 91.8k
5
votes
What are parabolic bundles good for?
They arise in analytic theory of differential equations with regular singularities, Riemann Hilbert problem and Painleve equations.
MR1924757
Biswas, Indranil
A criterion for the existence of a flat c …
- 4,713
4
votes
Can the theory of elliptic functions developed from purely geometric considerations?
Some elementary parts of the theory of elliptic functions can indeed be developed in this way. To those books listed by Alexey Ustinov I can add a large treatise by G. Halphen, Traité des fonctions el …
- 35.4k
32
votes
How would a topologist explain "every Riemann surface of genus $g$ is hyperelliptic if and o...
A 19th century topologist would explain this by dimension count. By Riemann-Hurwitz, a surface of genus $g$ covering the sphere
with $2$ sheets has $2g+2$ ramification points which gives $2g-1$ free c …
- 105k
6
votes
Accepted
How can I show $\{\mathbf{x}: \dim (\ker M_1(\mathbf{x}) \cap \ker M_2(\mathbf{x})) \geq C \...
Evidently, $\mathrm{Ker} M_1\cap \mathrm{Ker} M_2=\mathrm{Ker}(M_1,M_2)$,
where $(M_1,M_2)=:M$ is the $2m\times m$ matrix obtained by putting $M_1,M_2$
together ($k$-th column of $M$ consists the of t …
- 91.8k
4
votes
Algebraic closure of $\mathbb{C}(t)$
Elements of $\overline{C(t)}$ are not really functions since they do not have a common domain that would allow to add and multiply them. One way to think of $\overline{C(t)}$ is to consider the field …
- 91.8k
5
votes
What is the state-of-the-art for solving polynomials systems over fields that are not algebr...
For the real field:
MR2830310
Sottile, Frank
Real solutions to equations from geometry.
University Lecture Series, 57. American Mathematical Society, Providence, RI, 2011.
MR2275625 Mikhalkin, Grigo …
- 3,065