The sharp lower bound for the volume of 3-folds of general type with \chi(\Co{X})=1

Let $V$ be a smooth projective 3-fold of general type. Denote by $K^3$, a rational number, the self-intersection of the canonical sheaf of any minimal model of $V$. One defines $K^3$ as a canonical volume of $V$. The paper is devoted to proving the sharp lower bound $K^3\ge 1\mathrm{/}420$ which can be reached by an example: $X_{46}\subseteq \mathbb{P}(4,5,6,7,23)$.