Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivariant deformations of algebraic varieties with an action of an
  algebraic torus of complexity 1   Let $X$ be a 3-dimensional affine variety with a faithful action of a
2-dimensional torus $T$. Then the space of first order infinitesimal
deformations $T^1(X)$ is graded by the characters of $T$, and the zeroth graded
component $T^1(X)_0$ consists of all equivariant first order (infinitesimal)
deformations.
  Suppose that using the construction of such varieties from [1], one can
obtain $X$ from a proper polyhedral divisor $\mathscr D$ on $\mathbb P^1$ such
that the tail cone of (any of) the used polyhedra is pointed and
full-dimensional, and all vertices of all polyhedra are lattice points. Then we
compute $\dim T^1(X)_0$ and find a formally versal equivariant deformation of
$X$. We also establish a connection between our formula for $\dim T^1(X)_0$ and
known formulas for the dimensions of the graded components of $T^1$ of toric
varieties.

15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat