32 citations · 86 across the 17 of their papers we have counts for
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Nonrational Symplectic Toric Reduction
Fiammetta Battaglia, Elisa Prato
In this article, we introduce symplectic reduction in the framework of nonrational toric geometry. When we specialize to the rational case, we get symplectic reduction for the acti…
Hirzebruch surfaces in a one-parameter family
Fiammetta Battaglia, Elisa Prato, Dan Zaffran
We introduce a family of spaces, parametrized by positive real numbers, that includes all of the Hirzebruch surfaces. Each space is viewed from two distinct perspectives. First, as…
Toric Geometry of the Regular Convex Polyhedra
Fiammetta Battaglia, Elisa Prato
In this article, we describe symplectic and complex toric spaces associated to the five regular convex polyhedra. The regular tetrahedron and the cube are rational and simple, the…
Nonrational Symplectic Toric Cuts
Fiammetta Battaglia, Elisa Prato
In this article we extend cutting and blowing up to the nonrational symplectic toric setting. This entails the possibility of cutting and blowing up for symplectic toric manifolds…
Ammann Tilings in Symplectic Geometry
Fiammetta Battaglia, Elisa Prato
In this article we study Ammann tilings from the perspective of symplectic geometry. Ammann tilings are nonperiodic tilings that are related to quasicrystals with icosahedral symme…
The Symplectic Penrose Kite
Fiammetta Battaglia, Elisa Prato
The purpose of this article is to view the Penrose kite from the perspective of symplectic geometry.
The Symplectic Geometry of Penrose Rhombus Tilings
Fiammetta Battaglia, Elisa Prato
The purpose of this article is to view Penrose rhombus tilings from the perspective of symplectic geometry. We show that each thick rhombus in such a tiling can be naturally associ…
Convex Polytopes and Quasilattices from the Symplectic Viewpoint
Fiammetta Battaglia
We construct, for each convex polytope, possibly nonrational and nonsimple, a family of compact spaces that are stratified by quasifolds, i.e. each of these spaces is a collection…
Nonrational, nonsimple convex polytopes in symplectic geometry
Fiammetta Battaglia, Elisa Prato
In this research announcement we associate to each convex polytope, possibly nonrational and nonsimple, a family of compact spaces that are stratified by quasifolds, i.e. the strat…