LDP polygons and the number 12 revisited

Ulrike Bücking; Christian Haase; Karin Schaller; Jan-Hendrik de Wiljes

LDP polygons and the number 12 revisited

Combinatorics 2023-09-06 v1 Algebraic Geometry Number Theory

Authors: Ulrike Bücking , Christian Haase , Karin Schaller , Jan-Hendrik de Wiljes

Abstract

We give a combinatorial proof of a lattice point identity involving a lattice polygon and its dual, generalizing the formula $area(\Delta) + area(\Delta^*) = 6$ for reflexive $\Delta$ . The identity is equivalent to the stringy Libgober-Wood identity for toric log del Pezzo surfaces.

Keywords

lattice polygon dual polygon lattice point identity reflexive polygon log del pezzo surface combinatorial proof

Cite

@article{arxiv.2309.02339,
  title  = {LDP polygons and the number 12 revisited},
  author = {Ulrike Bücking and Christian Haase and Karin Schaller and Jan-Hendrik de Wiljes},
  journal= {arXiv preprint arXiv:2309.02339},
  year   = {2023}
}

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20 pages, 8 figures

LDP polygons and the number 12 revisited

Abstract

Keywords

Cite

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