Andrés Jaramillo-Puentes

During my postdoctoral position in the UDE, the focus of my research has been the understanding of a possible geometric definition of the Block-Göttsche and the Göttsche-Schroeter invariants.

In a first instance, I computed generated series for the coefficients of fixed codegree of the Block-Göttsche invariants in terms of the characteristic classes of some toric surfaces with simple Newton polygons in order to show that a universal generated series exist. This work is in progress and it is aimed to the restricted case of of the complex projective plane, Hirzebruch surfaces and weighted complex projective plane as a first step. Establishing a relationship between the coefficients of this generating series and the characteristic classes of the surfaces within this family would allow us to conjecture geometric properties for the refined invariants of more general toric surfaces.

In a second instance, I computed alternative refinements to the classical Gromov-Witten enumeration of plane complex curves based on classical algebro-geometric invariants of curves, working towards a parallel with the Block-Göttsche invariants. However, these computations do not coincide with the combinatorial refinement we had calculated.

Project related publications

Project related preprints

Works in progress

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This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 832833)