• Torsionfree Sheaves over a Nodal Curve of Arithmetic Genus One

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/118/01/0081-0098

• # Keywords

Torsionfree sheaves; nodal curve; stability.

• # Abstract

We classify all isomorphism classes of stable torsionfree sheaves on an irreducible nodal curve of arithmetic genus one defined over $\mathbb{C}$. Let 𝑋 be a nodal curve of arithmetic genus one defined over $\mathbb{R}$, with exactly one node, such that 𝑋 does not have any real points apart from the node. We classify all isomorphism classes of stable real algebraic torsionfree sheaves over 𝑋 of even rank. We also classify all isomorphism classes of real algebraic torsionfree sheaves over 𝑋 of rank one.

• # Author Affiliations

1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 4
September 2019