Seminar

The Göttsche conjecture, now a theorem, states that the degree of the Severi locus of k-nodal curves in a linear system can be expressed universally as a polynomial in the four Chern numbers. Kleiman and Piene have formulated a family and cycle version of this conjecture. More precisely, it states that for a relative effective divisor on a family of surfaces, there exists a natural cycle on the base, enumerating the k-nodal fibres of the divisor. It's class can be expressed universally in the Chern data of the surface and the divisor. Using the BPS-calculus of Pandharipande and Thomas, we will prove the conjecture.