Mathematics – Algebraic Geometry
Scientific paper
2009-05-12
Mathematics
Algebraic Geometry
30 pages
Scientific paper
Let C be a projective Gorenstein curve over an algebraically closed field of characteristic 0. A generalized linear system on C is a pair (I,f) consisting of a torsion-free, rank-1 sheaf I on C and a map of vector spaces f to the space of global sections of I. If the system is nondegenerate on every irreducible component of C, we associate to it a 0-cycle W, its Weierstrass cycle. Then we show that for each one-parameter family of curves C(t) degenerating to C, and each family of linear systems (L(t),f(t)) along C(t), with L(t) invertible, degenerating to (I,f), the corresponding Weierstrass divisors degenerate to a subscheme whose associated 0-cycle is W. We show that the limit subscheme contains always an "intrinsic" subscheme, canonically associated to (I,f), but the limit itself depends on the family L(t).
Esteves Eduardo
Nogueira Patricia
No associations
LandOfFree
Generalized linear systems on curves and their Weierstrass points 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 Generalized linear systems on curves and their Weierstrass points, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalized linear systems on curves and their Weierstrass points will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-337087