Vector Bundles and Torsion Free Sheaves on Degenerations of Elliptic Curves

By L. Bodnarchuk, I. Burban, Y. Drozd, Gert-Martin Greuel. 2006

50 citations recorded by the source corpus.

In this paper we give a survey about the classification of vector bundles and torsion free sheaves on degenerations of elliptic curves. Coherent sheaves on singular curves of arithmetic genus one can be studied using the technique of matrix problems or via Fourier-Mukai transforms, both methods are discussed here. Moreover, we include new proofs of some classical results about vector bundles on elliptic curves.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4683637d9fd5dff8a90c1636eff12ee69f7c68fc

Citations in the corpus

• Stability conditions and curve counting invariants on Calabi–Yau 3-folds (2011, unknown): “ten as E ∼= i p∗E (86) ′, for some stable sheaf E′ on an elliptic fiber π−1(p) for some p ∈ S. Here ip : π−1(p) → X is the inclusion. By the classification of stable sheaves on the fibers of π given in [8], we have Ms (87) n,m(ωX) = ∅, if g.c.d.(n,m) > 1. Assume that g.c.d.(n,m) = 1. Let Y → S, be t”