140 citations · 603 across the 27 of their papers we have counts for
7 papers · 1 filter
A conjectural generating function for numbers of curves on surfaces
Lothar Goettsche
I give a conjectural generating function for the numbers of -nodal curves in a linear system of dimension on an algebraic surface. It reproduces the results of Vainsencher f…
Euler number of the compactified Jacobian and multiplicity of rational curves
Barbara Fantechi, Lothar Göttsche, Duco van Straten
We show that the Euler number of the compactified Jacobian of a rational curve with locally planar singularities is equal to the multiplicity of the -constant stratum in the…
Jacobi forms and the structure of Donaldson invariants for 4-manifolds with b_+=1
Lothar Göttsche, Don Zagier
We prove structure theorems for the Donaldson invariants of 4-manifolds with b_+=1, similar to those of Kronheimer and Mrowka in the case b_+>1: We show that for a 4-manifold with…
The quantum cohomology of blow-ups of P^2 and enumerative geometry
Lothar Göttsche, Rahul Pandharipande
We compute the Gromov-Witten invariants of the projective plane blown up in r general points. These are determined by associativity from r+1 intial values. Applications are given t…
Wall-crossing formulas, Bott residue formula and the Donaldson invariants of rational surfaces
Geir Ellingsrud, Lothar Göttsche
We study the Donaldson invariants of rational surfaces and their dependence on the chambers in the ample cone. We build on a previous joint paper in which we have expressed the cha…
Modular forms and Donaldson invariants for 4-manifolds with
Lothar Göttsche
We study the Donaldson invariants of simply connected -manifolds with , and in particular the change of the invariants under wall-crossing. We assume the conjecture of Ko…