The motive of some moduli spaces of vector bundles over a curve

Details The motive of some moduli spaces of vector bundles over a curve The motive of some moduli spaces of vector bundles over a curve

1995-01-31

arxiv.org/abs/alg-geom/9501013v1

Mathematics

Algebraic Geometry

21 pages AMS-TEX

Scientific paper

We study the motive of the moduli spaces of semistable rank two vector bundles over an algebraic curve. When the degree is odd the moduli space is a smooth projective variety, we obtain the absolute Hodge motive of this, and in particular the Hodge-Poincare polynomial. When the degree is even the moduli space is a singular projective variety, we compute pure Euler characteristics and show that only two weights can occur in each cohomology group, we also see that its cohomology is pure up to a certain degree. As a by-product we obtain the isogeny type of some intermediate jacobians of the moduli spaces.

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