Tagged Questions

3
votes
1answer
125 views

“Degree” of a Fano Scheme of a projective variety

Consider subschemes $F$ of the Grassmannian $\mathbb{G}(k,n)$ satisfying the condition that each point of $\mathbb{P}^n$ is contained in only finitely many of the $k$-planes in $F$ …
3
votes
2answers
306 views

Conics in the quadric line complex

Hello, I apologize in advance if this question is misguided somehow, since my algebraic geometry is pretty shaky. I am wondering if there is a way to understand all the conics in …
5
votes
3answers
504 views

Thom polynomial for contact algebraic structures

Let's consider a algebraic contact structure $P$ on $\mathbb CP^3$ and a algebraic curve $C$ degree $d$ and genus $g$. Let's assume that contact structure has degree $p$ (see http: …
1
vote
1answer
180 views

Riemann-Roch and dim of deformation space.

Let's consider curve $C\subset \mathbb P^n$ of degree $d$ and genus $g$. We want to calculate dimension of deformation space of $C$, i.e. $h^0(C,L)$ where $L$ is the normal bundle. …
7
votes
1answer
308 views

Incidence Correspondence

A useful tool in Algebraic Geometry is the incidence correspondence. Loosely speaking, it is a set of the form $$\{(p,X): p \text{ a fixed dimension subscheme of } Y \text{ and } X …
3
votes
1answer
401 views

Is P^2 important in Kontsevich’s recursion formula?

There is a famous recursion formula by Kontsevich to find the number of genus zero degree $d$ curves in $\mathbb{CP}^2$ through $3d-1$ points. My question is the following: Let $ …
0
votes
0answers
191 views

Exercise in cosmic Galois theory on the quintic threefolds

Considering the MO question Connes-Kreimer Hopf algebra and cosmic Galois group, can you calculate the cosmic Galois group of a "bundle" over a quintic threefold and relate it with …
5
votes
2answers
977 views

Nagata’s conjecture, Seshadri constant

What is it known now about Nagata's conjecture and Seshadri constant (http://en.wikipedia.org/wiki/Nagata%27s_conjecture_on_curves and http://en.wikipedia.org/wiki/Seshadri_constan …
11
votes
3answers
830 views

Counting restricted polyominoes

I would like to count the polyominoes of $n$ squares that satisfy several restrictions: Each is convex: every horizontal, or vertical line, meets the shape in either a single seg …
15
votes
7answers
1k views

Higher Dimensional Gromov-Witten Theories

So, 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" th …
3
votes
1answer
265 views

Hurwitz numbers and Frobenius manifolds

Generating functions of the Gromov-Witten invariants (as well as some other important partition functions) are known to be related to the Frobenius manifold structure. Are there an …
8
votes
1answer
361 views

Multiple Hodge integrals and integrability

It is known that a generating function of the linear Hodge integrals is a tau function of the KP hierarchy, namely a one-parameter deformation of the Kontsevich-Witten tau-function …
2
votes
0answers
127 views

Are there ways to make low degree checks for enumerative formulas except for curves in CP^2?

This is a concrete question in Enumerative geometry. Let $S$ be a compact complex surface and $L\rightarrow S$ a holomorphic line bundle. Let $$ \delta_d = \text{dim}~ \mathbb{ …
0
votes
1answer
209 views

What is the simplest way to show that a section of a vector bundle is transverse to the zero set

Let $\mathcal{D} \approx \mathbb{P}^{\delta_d}$, be the space of homogeneous degree $d$ polynomials in three variables $[X,Y,Z] \in \mathbb{P}^2$ upto scaling, where $\delta_d = …
5
votes
1answer
461 views

Embedding $G(2,n)$ into $G(k,n)$

Let $$M=\begin{pmatrix} u_1 & u_2 & \ldots & u_n \\ v_1 & v_2 & \ldots & v_n \\ \end{pmatrix}$$ be a $2 \times n$ matrix. Define $\nu(M)$ to be the $k \tim …

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