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

Rapoport, M.

Jahresber. Dtsch. Math.-Ver. 99, No. 4, 164-180 (1997).

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.

Reviewer: D.Laksov (Stockholm)

MSC:

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

Keywords:

moduli space of vector bundles; Riemann surfaces; filtered vector spaces; semi-stability; Poincaré series