All Outputs (3)

Fano polytopes (2012)
Book Chapter
Kasprzyk, A. M., & Nill, B. (2012). Fano polytopes. In A. Rebhan, L. Katzarkov, J. Knapp, R. Rashkov, & E. Scheidegger (Eds.), Strings, gauge fields, and the geometry behind: the legacy of Maximilian Kreuzer (349-364). World Scientific. https://doi.org/10.1142/9789814412551_0017

Fano polytopes are the convex-geometric objects corresponding to toric Fano varieties. We give a brief survey of classification results for different classes of Fano polytopes.

Reflexive polytopes of higher index and the number 12 (2012)
Journal Article
Kasprzyk, A. M., & Nill, B. (2012). Reflexive polytopes of higher index and the number 12. Electronic Journal of Combinatorics, 19(3), Article P9

We introduce reflexive polytopes of index l as a natural generalisation of the notion of a reflexive polytope of index 1. These l-reflexive polytopes also appear as dual pairs. In dimension two we show that they arise from reflexive polygons via a ch... Read More about Reflexive polytopes of higher index and the number 12.

Minkowski polynomials and mutations (2012)
Journal Article
Akhtar, M., Coates, T., Galkin, S., & Kasprzyk, A. M. (2012). Minkowski polynomials and mutations. Symmetry, Integrability and Geometry: Methods and Applications, 8, Article 094, pp. 707. https://doi.org/10.3842/SIGMA.2012.094

Given a Laurent polynomial f, one can form the period of f: this is a function of one complex variable that plays an important role in mirror symmetry for Fano manifolds. Mutations are a particular class of birational transformations acting on Lauren... Read More about Minkowski polynomials and mutations.