On the geography of threefolds of general type

Jungkai A. Chen, Christopher D. Hacon

Let $X$ be a complex nonsingular projective 3-fold of general type. We show that there are positive constants $c$, $c^{\prime }$ and $m_1$ such that $χ(ω_X)\geq -c\Vol (X)$ and $P_m(X)\geq…