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Riemannian metrics on complemements of subvarieties

Ponente: Matthew Stover
Institución: Temple University
Tipo de Evento: Investigación
Cuándo 05/11/2015
de 13:00 a 14:30
Dónde Salon de Seminarios Graciela Salicrup
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Let C be a smooth complex projective curve and D a finite, possibly empty, collection of distinct points on C. Classical uniformization says that M = C-D admits a complete metric of finite volume and constant curvature -1 precisely when the Euler number e(M) is negative. In other words, there is a purely topological necessary and sufficient condition.

I will discuss topological methods for proving existence of a metric of constant holomorphic sectional curvature -1 on the complement of curves in a smooth complex projective surface, and some applications. I will mainly focus on an interesting example due to Hirzebruch. This is mostly joint with Luca Di Cerbo.