Freeness of Pluricanonical Linear System on Smooth Minimal n-folds of General Type

Let $X$ be a smooth minimal projective variety of general type of dimension $n$ over $\mathbb{C}$. We prove that $\mathrm{\mid }\frac{n^2+n+2}{2}{K}_X\mathrm{\mid }$ is base point free. This gives a bound for the pluricanonical case of Fujita Freeness Conjecture with merely nef and big divisor. Let $X$ be a smooth projective variety of dimension $n$ and $B$ be a nef and big Cartier divisor. We also prove that $\mathrm{Bs}\mathrm{\mid }{K}_X+mB\mathrm{\mid }\subseteq {\mathbf{B}}_{+}(B)$ for every integer $m\ge m_n\sim n^2\mathrm{/}\log n$, where ${\mathbf{B}}_{+}(B)$ is the augmented base locus.