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Results tagged with enumerative-geometry
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user 297
6
votes
Accepted
How do the number of plane curves over a finite field of a fixed genus increase with the deg...
Fix $g$, the genus, and $q$, the order of $k$.
$N(d,g)$ should be $\approx C q^{3d}$, where $C$ is some constant dependent on $q$ and $g$. (Note that my $C$ has absorbed the $q^{-4}$ in Felipe's answe …
- 156k
7
votes
Accepted
Riemann-Roch and dim of deformation space.
Let's start by stating Riemmann-Roch for vector bundles: If $C$ is a smooth projective curve of genus $g$, and $E$ is a vector bundle of rank $r$ and degree $\delta$, then $h^0(C,E) - h^1(C,E) = \delt …
- 156k
7
votes
Higher-dimensional Gromov-Witten theories
Alexeev's and Knutson's moduli space of branch varieties in
Complete moduli spaces of branchvarieties, Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2010, Issue 639, Pages …
- 156k
5
votes
Interaction of topology and the Picard group of Algebraic surfaces
I worry that the other answers may be giving too much detail. What is going on is that there are linear relations between the classes of the lines so that, although they are 27 lines in the cubic surf …
- 156k
11
votes
Accepted
Is there a tropical geometric proof for counting genus g curves in any n dimensional project...
Here is an attempt at an overview of tropical curve counts by someone who has been involved in the story for a while but certainly hasn't followed everything that has happened. I look forward to being …
- 156k