All Outputs (3)

Laurent inversion (2019)
Journal Article
Coates, T., Kasprzyk, A., & Prince, T. (2019). Laurent inversion. Pure and Applied Mathematics Quarterly, 15(4), 1135–1179. https://doi.org/10.4310/PAMQ.2019.v15.n4.a5

We describe a practical and effective method for reconstructing the deformation class of a Fano manifold X from a Laurent polynomial f that corresponds to X under Mirror Symmetry. We explore connections to nef partitions, the smoothing of singular to... Read More about Laurent inversion.

Gorenstein Formats, Canonical and Calabi–Yau Threefolds (2019)
Journal Article
Brown, G., Kasprzyk, A., & Zhu, L. (2022). Gorenstein Formats, Canonical and Calabi–Yau Threefolds. Experimental Mathematics, 31(1), 146-164. https://doi.org/10.1080/10586458.2019.1592036

Gorenstein formats present the equations of regular canonical, Calabi–Yau and Fano varieties embedded by subcanonical divisors. We present a new algorithm for the enumeration of these formats based on orbifold Riemann-Roch and knapsack packing-type a... Read More about Gorenstein Formats, Canonical and Calabi–Yau Threefolds.

Ehrhart polynomial roots of reflexive polytopes (2019)
Journal Article
KASPRZYK, A., Hegedus, G., & Higashitani, A. (2019). Ehrhart polynomial roots of reflexive polytopes. Electronic Journal of Combinatorics, 26(1), Article P1.38

Recent work has focused on the roots z∈C of the Ehrhart polynomial of a lattice polytope P. The case when Rz=−1/2 is of particular interest: these polytopes satisfy Golyshev's "canonical line hypothesis". We characterise such polytopes when dim(P)≤7.... Read More about Ehrhart polynomial roots of reflexive polytopes.