Embedded Files
Chow Ring of Toric Arrangements
The Project
The Project
The Principal Investigator of this project "CRoTA" is prof. Roberto Pagaria. The project will begin in mid-September 2026 and end in August 2029, at the Alma Mater Studiorum Università di Bologna.
It is funded by the FIS 2 (Fondo Italiano per la Scienza) with 1.321.804 € by the Italian Ministry of University and Research MUR.
The fan of a good toric variety
Milestone A) Toric arrangements.
Milestone A) Toric arrangements.
The project will start with an in-depth study of toric arrangements and toric wonderful model. The focus will be on the algebraic invariants that has been useful for hyperplane arrangements (i.e., Chow ring and Chern classes). In particular, the research group will investigate a combinatorial description of these invariants.
Milestone B) Non realizable case.
Milestone B) Non realizable case.
The second step consists in extending the Chow ring and the Chern classes to the non-realizable setting. It is necessary to clarify precisely what is meant by “non-realizable.” Four different axiomatizations of the combinatorial framework have been proposed (arithmetic matroids, matroids over Z, Z-semimatroids, and matroid schemes), and it will be necessary to determine the most suitable setting in which to work.
A toric arrangement on a compact torus
A log-concave sequence (in log-scale)
Milestone C) Applications.
Milestone C) Applications.
The first application of the work in Milestones A and B will be the investigation of log-concavity and unimodularity of sequence of coefficients of polynomials associated to arithmetic matroid. Determining now which polynomials to consider is premature.
Page updated
Google Sites
Report abuse