Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized linear systems on curves and their Weierstrass points   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).

12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat