5 papers
Discrete geometry of Cox rings of blow-ups of
Mara Belotti, Marta Panizzut
We prove quadratic generation for the ideal of the Cox ring of the blow-up of at points, solving a conjecture of Lesieutre and Park. To do this we compute Khovan…
The enumerative geometry of cubic hypersurfaces: point and line conditions
Mara Belotti, Alessandro Danelon, Claudia Fevola +1
In order to count the number of smooth cubic hypersurfaces tangent to a prescribed number of lines and passing through a given number of points, we construct a compactification of…
Algebraic Degrees of 3-Dimensional Polytopes
Mara Belotti, Michael Joswig, Marta Panizzut
Results of Koebe (1936), Schramm (1992), and Springborn (2005) yield realizations of -polytopes with edges tangent to the unit sphere. Here we study the algebraic degrees of suc…
Graph invariants from the topology of rigid isotopy classes
Mara Belotti, Antonio Lerario, Andrew Newman
We define a new family of graph invariants, studying the topology of the moduli space of their geometric realizations in Euclidean spaces, using a limiting procedure reminiscent of…
Real Lines on Random Cubic Surfaces
Rida Ait El Manssour, Mara Belotti, Chiara Meroni
We give an explicit formula for the expectation of the number of real lines on a random invariant cubic surface, i.e. a surface defined by a random gaussia…