Geodesic
LDP polygons and the number 12 revisited
Ulrike Bücking1 ; Christian Haase1 ; Karin Schaller1 ; Jan-Hendrik de Wiljes2
1Institut für Mathematik, Freie Universität Berlin
2Freie Universität Berlin
The electronic journal of combinatorics, Tome 32 (2025) no. 3
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We give a combinatorial proof of a lattice point identity involving a lattice polygon and its dual, generalizing the formula $\operatorname{area}\left(\Delta \right) + \operatorname{area}\left(\Delta^* \right) = 6$ for reflexive $\Delta$. The identity is equivalent to the stringy Libgober-Wood identity for toric log del Pezzo surfaces.
DOI : 10.37236/12783
Classification : 52B20, 14M25, 11F20, 32J15
Mots-clés : LDP polygons, log del Pezzo surfaces, toric geometry, normalized volume

Ulrike Bücking  1   ; Christian Haase  1   ; Karin Schaller  1   ; Jan-Hendrik de Wiljes  2

1 Institut für Mathematik, Freie Universität Berlin
2 Freie Universität Berlin 
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Ulrike Bücking; Christian Haase; Karin Schaller; Jan-Hendrik de Wiljes. LDP polygons and the number 12 revisited. The electronic journal of combinatorics, Tome 32 (2025) no. 3. doi: 10.37236/12783

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