6 papers · 1 filter
Intrinsic enumerative mirror symmetry: Takahashi's log mirror symmetry for revisited
Michel van Garrel, Helge Ruddat, Bernd Siebert
Let be a smooth cubic in the projective plane . Nobuyoshi Takahashi formulated a conjecture that expresses counts of rational curves of varying degree in $\mathbb…
Stable maps to Looijenga pairs: orbifold examples
Pierrick Bousseau, Andrea Brini, Michel van Garrel
In arXiv:2011.08830 we established a series of correspondences relating five enumerative theories of log Calabi-Yau surfaces, i.e. pairs with a smooth projective comple…
Log BPS numbers of log Calabi-Yau surfaces
Jinwon Choi, Michel van Garrel, Sheldon Katz +1
Let be a log Calabi-Yau surface pair with a smooth divisor. We define new conjecturally integer-valued counts of -curves in . These log BPS numbers…
Local BPS Invariants: Enumerative Aspects and Wall-Crossing
Jinwon Choi, Michel van Garrel, Sheldon Katz +1
We study the BPS invariants for local del Pezzo surfaces, which can be obtained as the signed Euler characteristic of the moduli spaces of stable one-dimensional sheaves on the sur…
Local and relative BPS state counts for del Pezzo surfaces
Michel van Garrel
Relative BPS state counts for log Calabi-Yau surface pairs were introduced by Gross-Pandharipande-Siebert. We describe how in the case of del Pezzo surfaces they are linearly relat…
On a conjecture by N. Takahashi on log mirror symmetry for the projective plane
Michel van Garrel
The relationship between local and relative BPS state counts is explored in light of a conjecture on log mirror symmetry by N. Takahashi.