Mathematics – Algebraic Geometry
Scientific paper
2006-03-10
Comm. Algebra 36 (2008), no. 8, 3032 - 3041
Mathematics
Algebraic Geometry
AMS-LaTeX, 12 pages, minor changes. To appear in Comm. Algebra
Scientific paper
10.1080/00927870802110797
Let k be an algebraically closed field of characteristic 0, and let $A = k[x,y]/(f)$ be a quasi-homogeneous plane curve. We show that for any graded torsion free A-module M, there exists a natural graded integrable connection, i.e. a graded A-linear homomorphism $\nabla: \operatorname{Der}_k(A) \to \operatorname{End}_k(M)$ that satisfy the derivation property and preserves the Lie product. In particular, a torsion free module N over the complete local ring $B = \hat A$ admits a natural integrable connection if A is a simple curve singularity, or if A is irreducible and N is a gradable module.
No associations
LandOfFree
Connections on modules over quasi-homogeneous plane curves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Connections on modules over quasi-homogeneous plane curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Connections on modules over quasi-homogeneous plane curves will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-114825