All Questions
Tagged with enumerative-geometry ag.algebraic-geometry
57 questions
13
votes
1
answer
2k
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Who streamlined Kontsevich's count of rational curves?
Let $N_d$ denote the number of rational curves in $\mathbf P^2$ passing through $3d-1$ points in general position. Maxim Kontsevich discovered a famous recursion for these numbers:
$$ N_d = \sum_{k+l =...
- 40.2k
5
votes
2
answers
647
views
Is anything known about the enumeration of degree d, genus g curves in CP^2 where g >1 ?
I wanted to know if there is something analogous to Kontsevich's recursion formula for
enumeration of genus zero curves in $\mathbb{C}\mathbb{P}^2$, for higher genus curves.
There is a
similar ...
- 3,245
2
votes
1
answer
643
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Computing 3 points Gromov-Witten invariants of the Grassmannian
This is from an exercise in Koch, Vainsencher - An invitation to quamtum cohomology.
Background
The exercise asks to compute the 3-points Gromov-Witten invariants of the Grassmannian $G = \mathop{Gr}...
- 14.7k
6
votes
1
answer
966
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Chow Ring of Moduli Space of Abelian Varieties
Is there a good reference for the structure of the Chow ring of $\mathcal{A}_g$, the moduli space of complex principally polarized abelian varieties? More generally, references for the intersection ...
- 16k
2
votes
0
answers
396
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Noether-Lefschetz locus in enumerative geometry.
It is well known that if you have a smooth quartic surface $X\subset \mathbb{P}^3$, it may or may not have lines in it. Indeed, $X$ has the following options, 64 (the maximal number), 32, 16, or none.
...
- 2,132
11
votes
5
answers
2k
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Classical Enumerative Geometry References
I want to start out by making this clear: I'm NOT looking for the modern proofs and rigorous statements of things.
What I am looking for are references for classical enumerative geometry, back before ...
- 16k
23
votes
7
answers
2k
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Higher-dimensional Gromov-Witten theories
A basic set-up in modern enumerative geometry is that you have some object $X$ (say, a "nice" stack, for whatever definition of "nice" you need) and then you want to "count&...
- 16k