Prüfer sheaves and generic sheaves over the weighted projective lines and elliptic curves

2013/05/28 by Jianmin Chen, Jinjing Chen, Chen, Jianmin +3
Mathematics · #14F05 #16G10 #16G60 #16G70 #18A30 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:14F05 #msc:16G10 #msc:16G60 #msc:16G70 #msc:18A30

paper · pdf · doi:10.48550/arxiv.1305.6399

27 pages

arxiv created 2015/07/07 · arxiv updated 2015/07/08

Abstract

In the present paper, we introduce the concepts of Prüfer sheaves and adic sheaves over a weighted projective line of genus one or an elliptic curve, show that Prüfer sheaves and adic sheaves can classify the category of coherent sheaves. Moreover, we describe the relationship between Prüfer sheaves and generic sheaves, and provide two methods to construct generic sheaves by using coherent sheaves and Prüfer sheaves.

Related

• Weighted projective lines and Riemann surfaces
• General sheaves over weighted projective lines
• Equivariant approach to weighted projective curves
• Introduction to coherent sheaves on weighted projective lines
• Coherent Sheaves on Singular Projective Curves with Nodal Singularities