Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effective behavior of multiple linear systems   We give optimal effective bounds for some well-known theorems on complex
algebraic surfaces, which are respectively due to Serre, Zariski (1962),
Castelnuovo (1897), Artin (1962, 1966), Benveniste (1984), Cutkosky and
Srinivas (1993). These theorems are about Riemann-Roch problem (on the behavior
of the function dim |nD| of n), vanishing theorems, base-point freeness and
k-very ampleness of the linear systems |nD| and |nA+L|, where D is effective, A
is nef and big and L is arbitrary. As a consequence, we obtain an effective
version of Matsusaka's big theorem, and we give also examples to show that our
bound is the best possible one.

30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ