\chapter*{Notation}

\begin{tabular}{ll}
$\Z,\Q,\R,\C$ & Integers, rational numbers, real numbers,
  complex numbers\\[2pt]
$\N$ & Semigroup of nonnegative integers $\{0,1,2,\dots\}$\\[2pt]
$\C^*$ & Multiplicative group of nonzero complex numbers $\C
  \setminus \{0\}$\\[2pt] 
$M$ & Character group of the torus $T_N$\\[2pt]
$\mr,M_\Q$ & Vector spaces $M\otimes_\Z \R, M\otimes_\Z \Q$ built
  from $M$\\[2pt] 
$N$ & Lattice of $1$-parameter subgroups of the torus $T_N$\\[2pt]
$\nr,N_\Q$ & Vector spaces $N\otimes_\Z \R, N\otimes_\Z \Q$ built from
  $N$\\[2pt] 
$\sigma$ & Rational convex polyhedral cone in $\nr$\\[2pt]
$\sigma^\vee$ & Dual cone of $\sigma$\\[2pt]
$\Sigma$ & Fan in $\nr$\\[2pt]
$\Sigma(r)$ & $r$-dimensional cones of $\Sigma$\\[2pt]
$\Sigma_{max}$ & Maximal cones of $\Sigma$\\[2pt]
$\ya$ & Affine toric variety of a finite set $\cA \subset M$\\[2pt]
$\xa$ & Projective toric variety of a finite set $\cA \subset M$\\[2pt]
$\xs$ & Toric variety of a fan $\Sigma$\\[2pt]
$\xp$ & Projective toric variety of a lattice polytope $P$\\[2pt]
$\mathrm{Cl}(X)$ & Divisor class group of a normal variety
  $X$\\[2pt]
$\mathrm{Pic}(X)$ & Picard group of a normal variety $X$
\end{tabular}
