Hi, I have the following question.

Reading about Seiberg-Witten theory one comes to realize that the \((a,a_D)\) are given by the quantities

\(\omega_A = \oint_A \lambda\) and \(\omega_B = \oint_B \lambda\)respectively. Ok, although I am not sure about what the physical motivation is, what I want to ask is why if our curve is, for example \(y= \sqrt{ (x-x_1)(x-x_2)(x-x_3)} \), this one form \(\lambda\)is defined as \(\frac{dx}{y}\).

More generally, why the cycles of the torus are defined like this. It certainly looks like a contour integral but I would like to ask a mathematical motivation for their specific form and maybe where to read about it explicitly.

Thanks a lot!