Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Normal presentation on Elliptic Ruled surfaces   In this article we determine exactly which line bundles on elliptic ruled
surface X are normally presented. In particular we see that numerical classes
of normally presented divisors form a convex set. (recall that Num(X) is
generated by the class of a minimal section C_0 and by the class of a fiber f
and that C_0 is ample.) As a corollary of the above result we show that Mukai's
conjecture is true for the normal presentation of the it adjoint linear series
for an elliptic ruled surface. In section 5 of this article, we show that if L
is normally presented on X then the homogeneous coordinate ring associated to L
is Koszul. We also give a new proof of the following result due to Butler: if
deg(L) \geq 2g+2 on a curve X of genus g, then L embeds X with Koszul
homogeneous coordinate ring.

30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga