Explicit birational geometry of threefolds of general type, I

Jungkai A. Chen; Meng Chen

Annales scientifiques de l'École Normale Supérieure (2010)

  • Volume: 43, Issue: 3, page 365-394
  • ISSN: 0012-9593

Abstract

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Let V be a complex nonsingular projective 3-fold of general type. We prove P 12 ( V ) : = dim H 0 ( V , 12 K V ) > 0 and P m 0 ( V ) > 1 for some positive integer m 0 ≤ 24 . A direct consequence is the birationality of the pluricanonical map ϕ m for all m ≥ 126 . Besides, the canonical volume Vol ( V ) has a universal lower bound ν ( 3 ) ≥ 1 63 · 126 2 .

How to cite

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Chen, Jungkai A., and Chen, Meng. "Explicit birational geometry of threefolds of general type, I." Annales scientifiques de l'École Normale Supérieure 43.3 (2010): 365-394. <http://eudml.org/doc/272136>.

@article{Chen2010,
abstract = {Let $V$ be a complex nonsingular projective 3-fold of general type. We prove $P_\{12\}(V):=\dim H^0(V, 12K_V)&gt;0$ and $P_\{m_0\}(V)&gt;1$ for some positive integer $m_0\le 24$. A direct consequence is the birationality of the pluricanonical map $\varphi _m$ for all $m\ge 126$. Besides, the canonical volume $\text\{Vol\}(V)$ has a universal lower bound $\nu (3)\ge \frac\{1\}\{63\cdot 126^2\}$.},
author = {Chen, Jungkai A., Chen, Meng},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {3-folds; plurigenus},
language = {eng},
number = {3},
pages = {365-394},
publisher = {Société mathématique de France},
title = {Explicit birational geometry of threefolds of general type, I},
url = {http://eudml.org/doc/272136},
volume = {43},
year = {2010},
}

TY - JOUR
AU - Chen, Jungkai A.
AU - Chen, Meng
TI - Explicit birational geometry of threefolds of general type, I
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2010
PB - Société mathématique de France
VL - 43
IS - 3
SP - 365
EP - 394
AB - Let $V$ be a complex nonsingular projective 3-fold of general type. We prove $P_{12}(V):=\dim H^0(V, 12K_V)&gt;0$ and $P_{m_0}(V)&gt;1$ for some positive integer $m_0\le 24$. A direct consequence is the birationality of the pluricanonical map $\varphi _m$ for all $m\ge 126$. Besides, the canonical volume $\text{Vol}(V)$ has a universal lower bound $\nu (3)\ge \frac{1}{63\cdot 126^2}$.
LA - eng
KW - 3-folds; plurigenus
UR - http://eudml.org/doc/272136
ER -

References

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