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Let $M$ be a two dimensional compact complex manifold and $A \in H_2(M, \mathbb{Z})$ a fixed homology class. Define a rational curve in $M$ to be $\textit{1-cuspidal}$ if the singularities of the ...

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 $S$ be a complex ...

This is a concrete question in Enumerative geometry. Let $S$ be a compact complex surface and $L\rightarrow S$ a holomorphic line bundle. Let $$ \delta_d = \text{dim}~ \mathbb{P}(H^0(S,L^d)) $$ ...

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 $\delta_d = \frac{d(d+3)}{2}$. ...

I wanted to know if anyone understood the details of the paper "Multisingularities, cobordisms, and enumerative geometry" available at the site http://www.mi.ras.ru/~kazarian/. In particular does ...