Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Castelnuovo-Mumford regularity of connected curves   In this paper we prove the Eisenbud-Goto conjecture for connected curves. We
also investigate the structure of connected curves for which this bound is
optimal. In particular, we construct connected curves of arbitrarily high
degree in projective 4-space having maximal regularity, but no extremal
secants. We also show that any connected curve in projective 3-space of degree
at least 5 that has no linear components and has maximal regularity has an
extremal secant.

29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th