scholarly journals Explicit birational geometry of threefolds of general type, I

2010 ◽  
Vol 43 (3) ◽  
pp. 365-394 ◽  
Author(s):  
Jungkai A. Chen ◽  
Meng Chen
1989 ◽  
Vol 314 (2) ◽  
pp. 825-825
Author(s):  
M. Beltrametti ◽  
A. Biancofiore ◽  
A. J. Sommese
Keyword(s):  

2014 ◽  
Vol 151 (6) ◽  
pp. 1041-1082 ◽  
Author(s):  
Jungkai A. Chen ◽  
Meng Chen

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.


1989 ◽  
Vol 314 (2) ◽  
pp. 825 ◽  
Author(s):  
M. Beltrametti ◽  
A. Biancofiore ◽  
A. J. Sommese
Keyword(s):  

Author(s):  
Zhuang-dan Guan ◽  
Pilar Orellana ◽  
Anthony Van

This is the fourth part of [6] on the existence of K¨ahler Einstein metrics of the general type I almost homogeneous manifolds of cohomogeneity one. We actually carry out all the results in [8] to the type I cases. In part II [14], we obtained a lot of new K¨ahler-Einstein manifolds as well as Fano manifolds without K¨ahler-Einstein metrics. In particular, by applying Theorem 15 therein, we have complete results in the Theorems 3 and 4 in that paper. However, we only have some partial results in Theorem 5 there. In this note, we shall give a report of recent progress on the Fano manifolds Nn,m when n > 15 and N′n,m when n > 4. We actually give two nice pictures for these two classes of manifolds. See our Theorems 1 and 2 in the last section. Moreover, we post two conjectures. Once we could solve these two conjectures, the question for these two classes of manifolds would be completely solved. With applying our results to the canonical circle bundles we also obtain Sasakian manifolds with or without Sasakian-Einstein metrics. That also give some open Calabi-Yau manifolds.


2008 ◽  
Vol 63 (12) ◽  
pp. 1395-1401 ◽  
Author(s):  
Ulrich Siemeling ◽  
Clemens Bruhn ◽  
Mario Meier ◽  
Christian Schirrmacher

A broad range of azobenzene derivates of the general type I-p-C6H4-N=N-p-C6H4-X (1) have been prepared. In the case of X = Ph (b), C≡C-Fc (e, Fc = ferrocenyl), OMe (g), Oi-Pr (i), and NMe2 (m), these compounds have been characterised by single-crystal X-ray structure analysis. In addition, the closely related 4-dimethylamino-1-(4-iodophenylazo)naphthalene 2 and 8-(4-iodophenylazo) quinoline 3 have also been prepared. Furthermore, the ferrocene derivative Fc-C≡C-p-C6H4- NH2 (4), which served as a starting material for the synthesis of I-p-C6H4-N=N-p-C6H4-p-C6H4- C≡C-Fc (1e), was prepared and structurally characterised by X-ray diffraction.


We have recently shown (‘Roy. Soc. Proc.,’ A, 1924, vol. 107, p. 80) that 1:2:3-triaminopropane forms co-ordination compounds with certain trivalent metals, such as cobalt and rhodium; these compounds are of the general type of bis -propanetriamine cobaltic chloride, [Co 2(NH 2 .CH(CH 2 .NH 2 ) 2 )] Cl 3 , in accordance with Werner’s theory of co-ordination. In these compounds the triaminopropane behaves in a similar way to ethylenediamine, each amino-group taking part in the formation of the co-ordinated radicle. It is thus seen that the grouping, NH 2 .CH 2 .CH.NH 2 , which is present twice in the triamino- propane molecule, behaves for co-ordination purposes in the same way as the molecule of ethylenediamine, NH 2 .CH 2 .CH 2 .NH 2 . This analogy in behaviour appears worthy of further investigation, and we have therefore studied the manner in which β β' β"-triaminotriethylamine, N(CH 2 .CH 2 .NH 2 ) 3 , co-ordinates with the metals; in this substance the grouping, NH 2 .CH 2 .CH 2 .N:, occurs three times, but it would seem that the presence of the three primary amino-groups has greatly diminished the basic properties of the tertiary amino-radicle, since Ristenpart (‘Ber.,’ 1896, vol. 29, p. 2530) obtained only salts in which the substance acts as a tribasic amine. It might thus be anticipated that co-ordinated salts of the type I would be formed.


2019 ◽  
Vol 190 (3) ◽  
pp. 559-587
Author(s):  
M. Măntoiu ◽  
M. Sandoval
Keyword(s):  

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