Variation of moduli spaces of coherent systems of dimension one and order one
arXiv:2104.06493
Abstract
We study the wall-crossing for moduli spaces of coherent systems of dimension one and order one on a smooth projective variety over the complex numbers. We compute the topological Euler characteristic of the moduli spaces in the particular case when the variety is a quadric surface, the first Chern class of the coherent systems is of the form (2,r) and the second Chern class is bounded from below by 3r + 1 and also by 4r - 8.
In v.2 the presentation has been improved and the results have been given their final form (section 7.3). Section 7.2 has also been added, containing the case r + t = 10. It turned out that Theorem 6.4 in v.1 is a consequence of a well-known result (Lemma 5.5 in v.2), so it has been eliminated from v.2. Section 2 in v.1 was mainly used in Theorem 6.4, so it was also eliminated