Analogies between moduli spaces of vector bundles and of flags
type: Item
instance of: scholarly article
title: Analogies between moduli spaces of vector bundles and of flags
zbMATH Open document ID: 0891.14010
published in: Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV)
publication date: 1997-11-18T00:00:00Z
review text: This most enjoyable text is the main contents of a talk at the DMV (Deutsche Mathematiker Vereinigung). The point of departure is the analogy between vector bundles on Riemann surfaces and \(\mathbb{Z}\)-filtered vector spaces. There is a similar analogy between the moduli space of vector bundles and the moduli space of \(\mathbb{Z}\)-filtered vector spaces satisfying semi-stability conditions. This is illustrated by the problem of determining the singular cohomology of both kinds of spaces. The presentation is like a leisurely walk through the field, with highlights at the combinatorial problems appearing in the determination of the Poincaré series.
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 14H60
Mathematics Subject Classification ID: 14M15
Mathematics Subject Classification ID: 14H55
zbMATH DE Number: 1088559
zbMATH Keywords: moduli space of vector bundles
zbMATH Keywords: Riemann surfaces
zbMATH Keywords: filtered vector spaces
zbMATH Keywords: semi-stability
zbMATH Keywords: Poincaré series
author: Michael Rapoport
reviewed by: Dan Laksov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1088559