Explicit birational geometry of 3-folds and 4-folds of general type, III.
In: Compositio Mathematica, Jg. 151 (2015-06-01), Heft 6, S. 1041-1082
Online
academicJournal
Zugriff:
Nonsingular projective 3-folds $V$ of general type can be naturally classified into 18 families according to the pluricanonical section index${\it\delta}(V):=\text{min}\{m\mid P_{m}\geqslant 2\}$ since $1\leqslant {\it\delta}(V)\leqslant 18$ due to our previous series (I, II). Based on our further classification to 3-folds with ${\it\delta}(V)\geqslant 13$ and an intensive geometrical investigation to those with ${\it\delta}(V)\leqslant 12$, we prove that $\text{Vol}(V)\geqslant \frac{1}{1680}$ and that the pluricanonical map ${\rm\Phi}_{m}$ is birational for all $m\geqslant 61$, which greatly improves known results. An optimal birationality of ${\rm\Phi}_{m}$ for the case ${\it\delta}(V)=2$ is obtained. As an effective application, we study projective 4-folds of general type with $p_{g}\geqslant 2$ in the last section. [ABSTRACT FROM PUBLISHER]
Titel: |
Explicit birational geometry of 3-folds and 4-folds of general type, III.
|
---|---|
Autor/in / Beteiligte Person: | Chen, Jungkai A. ; Chen, Meng |
Link: | |
Zeitschrift: | Compositio Mathematica, Jg. 151 (2015-06-01), Heft 6, S. 1041-1082 |
Veröffentlichung: | 2015 |
Medientyp: | academicJournal |
ISSN: | 0010-437X (print) |
DOI: | 10.1112/S0010437X14007817 |
Schlagwort: |
|
Sonstiges: |
|