Characterization of the 4-canonical birationality of algebraic threefolds
| dc.creator | Chen, Meng | |
| dc.creator | Zhang, De-Qi | |
| dc.date | 2007-03-20 | |
| dc.date.accessioned | 2026-07-07T07:52:53Z | |
| dc.date.available | 2026-07-07T07:52:53Z | |
| dc.description | In this article we present a 3-dimensional analogue of a well-known theorem of E. Bombieri (in 1973) which characterizes the bi-canonical birationality of surfaces of general type. Let $X$ be a projective minimal 3-fold of general type with $\mathbb{Q}$-factorial terminal singularities and the geometric genus $p_g(X)\ge 5$. We show that the 4-canonical map $ϕ_4$ is {\it not} birational onto its image if and only if $X$ is birationally fibred by a family $\mathscr{C}$ of irreducible curves of geometric genus 2 with $K_X\cdot C_0=1$ where $C_0$ is a general irreducible member in $\mathscr{C}$. | |
| dc.description | 25 pages, to appear in Mathematische Zeitschrift | |
| dc.identifier | https://arxiv.org/abs/math/0703593 | |
| dc.identifier | http://arxiv.org/abs/math/0703593 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/126045 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Characterization of the 4-canonical birationality of algebraic threefolds | |
| dc.type | text |