On the geometry of moduli spaces of coherent systems on algebraic curves

Details On the geometry of moduli spaces of coherent systems on algebraic curves On the geometry of moduli spaces of coherent systems on algebraic curves

2004-07-30

arxiv.org/abs/math/0407523v5

Mathematics

Algebraic Geometry

38 pages; v3. Appendix and new references added; v4. minor corrections, two added references; v5. final version, one typo corr

Scientific paper

Let $C$ be an algebraic curve of genus $g$. A coherent system on $C$ consists of a pair $(E,V)$, where $E$ is an algebraic vector bundle over $C$ of rank $n$ and degree $d$ and $V$ is a subspace of dimension $k$ of the space of sections of $E$. The stability of the coherent system depends on a parameter $\alpha$. We study the geometry of the moduli space of coherent systems for different values of $\alpha$ when $k\leq n$ and the variation of the moduli spaces when we vary $\alpha$. As a consequence, for sufficiently large $\alpha$, we compute the Picard groups and the first and second homotopy groups of the moduli spaces of coherent systems in almost all cases, describe the moduli space for the case $k=n-1$ explicitly, and give the Poincar\'e polynomials for the case $k=n-2$.

Affiliated with

Also associated with

No associations

Rating

On the geometry of moduli spaces of coherent systems on algebraic curves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the geometry of moduli spaces of coherent systems on algebraic curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the geometry of moduli spaces of coherent systems on algebraic curves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-504056