Seminario del 2024

Novembre
12
2024
Luca Schaffler
An explicit wall crossing for the moduli space of hyperplane arrangements
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA
algebra e geometria
The moduli space of hyperplanes in projective space has a family of geometric and modular compactifications that parametrize stable hyperplane arrangements with respect to a weight vector. Among these, there is a toric compactification that generalizes the Losev-Manin moduli space of points on the line. We study the first natural wall crossing that modifies this compactification into a non-toric one by varying the weights. As an application of our work, we show that any Q-factorialization of the blow up at the identity of the torus of the generalized Losev-Manin space is not a Mori dream space for a sufficiently high number of hyperplanes. Additionally, for lines in the plane, we provide a precise description of the wall crossing. This is joint work with Patricio Gallardo.
organizzato da: Enrico Fatighenti
nell'ambito del Progetto R.F.O. RFO2023 BIAGIOLI RICCARDO del prof. Riccardo Biagioli

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