Analogies between moduli spaces of vector bundles and of flags. (Analogien zwischen den Modulräumen von Vektorbündeln und von Flaggen.) (German) Zbl 0891.14010

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.


14H10 Families, moduli of curves (algebraic)
14H60 Vector bundles on curves and their moduli
14M15 Grassmannians, Schubert varieties, flag manifolds
14H55 Riemann surfaces; Weierstrass points; gap sequences