16 Novembre 2023 14:00 CET Aula seminari III piano
Roberto Pagaria Università degli Studi di Bologna

Cohomology ring of arrangement complements

Abstract The aim of this talk is to provide a uniform and intuitive description of the cohomology ring of arrangement complements. We introduce complex hyperplane arrangements and state the Orlik-Solomon theorem (1980). Then, we describe the real case and the Gelfand-Varchenko ring (1987). We define toric arrangements and present their cohomology ring (De Concini, Procesi 2005 and Callegaro, D’Adderio, Delucchi, Migliorini and P. 2020). Finally, we show a new technique to prove the Orlik-Solomon and De Concini-Procesi relations from the Gelfand-Varchenko ring. The technique applied to abelian arrangements provides a presentation of their cohomology.

This is a work in progress with Evienia Bazzocchi e Maddalena Pismataro.

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