6533b7d2fe1ef96bd125df90

RESEARCH PRODUCT

Vector Bundles and Torsion Free Sheaves on Degenerations of Elliptic Curves

Yuriy DrozdIgor BurbanGert-martin GreuelLesya Bodnarchuk

subject

AlgebraPure mathematicsElliptic curveMathematics::Algebraic GeometryLine bundleTorsion (algebra)Vector bundleSchoof's algorithmTwists of curvesSupersingular elliptic curveMathematicsCoherent sheaf

description

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.

yearjournalcountryeditionlanguage
2006-09-28
https://doi.org/10.1007/3-540-35480-8_3