Does any one understand the details of M Kazarian's work in enumerative geometry of $\mathbb{C}\mathbb{P}^2$ ? - MathOverflow

Does any one understand the details of M Kazarian's work in enumerative geometry of $\mathbb{C}\mathbb{P}^2$ ?

2010-08-20T01:27:14Z

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 any one follow how the author actually got all the expressions for $S_{A_k}$ on page 47. I think I follow the details of how he got $S_{A_1}$. But how does he get $S_{A_1^2}$ for instance?

Answer by Bob for Does any one understand the details of M Kazarian's work in enumerative geometry of $\mathbb{C}\mathbb{P}^2$ ?

2010-08-25T23:31:15Z

It's just a task in school math.: The Legendrean residual class R for A_1^2 is given by -u-3a_1 on page 44, and the recipe for substitution is noted on page 45: the answer is the coefficient of t^2 in the expansion of R.[M]. If your question means how he gets the residual classes, you have to learn about the contents, that would be more fruitful.