On the geography of threefolds of general type

TL;DR

This paper establishes bounds relating the Euler characteristic and pluricanonical sections of complex threefolds of general type, linking their topological and geometric properties through explicit inequalities.

Contribution

It provides new explicit inequalities connecting the Euler characteristic and pluricanonical volumes of threefolds of general type, advancing understanding of their geometric structure.

Findings

hi(_X)   \u00a9 ' \u00a9 'm^3 \u00a9 for all m  m_1.

Establishes positive constants c, c', m_1 for bounds on hi(_X) and P_m(X).

Links topological invariants with pluricanonical growth in threefolds.

Abstract

Let $X$ be a complex nonsingular projective 3-fold of general type. We show that there are positive constants $c$, $c'$ and $m_1$ such that $\chi (\omega _X)\geq -c\Vol (X)$ and $P_m(X)\geq c'm^3\Vol (X)$ for all $m\geq m_1$.