Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deformations of pairs (X,L) when X is singular   We give an elementary construction of the tangent-obstruction theory of the
deformations of the pair $(X,L)$ with $X$ a reduced local complete intersection
scheme and $L$ a line bundle on $X$. This generalizes the classical deformation
theory of pairs in case $X$ is smooth. A criteria for sections of $L$ to extend
is also given.

30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ