By Paula Tretkoff,Hans-Christoph Im Hof
This booklet introduces the idea of advanced surfaces via a complete examine finite covers of the projective airplane branched alongside line preparations. Paula Tretkoff emphasizes these finite covers which are unfastened quotients of the complicated two-dimensional ball. Tretkoff additionally contains historical past at the classical Gauss hypergeometric functionality of 1 variable, and a bankruptcy at the Appell two-variable F1 hypergeometric function.
The fabric during this publication begun as a collection of lecture notes, taken by way of Tretkoff, of a path given via Friedrich Hirzebruch at ETH Zürich in 1996. The lecture notes have been then significantly accelerated through Hirzebruch and Tretkoff over a few years. during this e-book, Tretkoff has accelerated these notes even additional, nonetheless stressing examples provided by way of finite covers of line preparations. The ebook is basically self-contained and foundational fabric is brought and defined as wanted, yet no longer handled in complete aspect. References to passed over fabric are supplied for readers.
Aimed at graduate scholars and researchers, this is often an available account of a hugely informative quarter of complicated geometry.
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Additional resources for Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51) (Mathematical Notes)
Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51) (Mathematical Notes) by Paula Tretkoff,Hans-Christoph Im Hof