scholarly journals The canonical ring of a 3-connected curve

2014 ◽  
Vol 25 (1) ◽  
pp. 37-51 ◽  
Author(s):  
Marco Franciosi ◽  
Elisa Tenni
Keyword(s):  
Canonical Ring

Derived Category and Canonical Bundle --II

2007 ◽  
Author(s):  
D. Huybrechts
Keyword(s):  
Hochschild Cohomology ◽  
Derived Categories ◽  
Kodaira Dimension ◽  
Derived Category ◽  
Canonical Bundle ◽  
Derived Equivalence ◽  
One Step ◽  
Canonical Ring ◽  
Special Case

Based on the work of Orlov, Kawamata, and others, this chapter shows that the (numerical) Kodaira dimension and the canonical ring are preserved under derived equivalence. The same techniques can be used to derive the invariance of Hochschild cohomology under derived equivalence. Going one step further, it is shown that the nefness of the canonical bundle is detected by the derived category. The chapter also studies the relation between derived and birational (or rather K-) equivalence. The special case of a central conjecture predicts that two birational Calabi-Yau varieties have equivalent derived categories.

On the Endomorphism Rings of Local Cohomology Modules

2010 ◽  
Vol 53 (4) ◽  
pp. 667-673 ◽  
Author(s):  
Kazem Khashyarmanesh
Keyword(s):  
Nonnegative Integer ◽  
Noetherian Ring ◽  
Local Cohomology ◽  
Ring Homomorphism ◽  
Endomorphism Rings ◽  
Commutative Noetherian Ring ◽  
Ring Of Fractions ◽  
Local Cohomology Modules ◽  
Canonical Ring ◽  
Cohomology Modules

AbstractLet R be a commutative Noetherian ring and a a proper ideal of R. We show that if n := gradeRa, then . We also prove that, for a nonnegative integer n such that = 0 for every i ≠ n, if for all i > 0 and z ∈ a, then is a homomorphic image of R, where Rz is the ring of fractions of R with respect to a multiplicatively closed subset ﹛z j | j ⩾ 0﹜ of R. Moreover, if HomR(Rz , R) = 0 for all z ∈ a, then is an isomorphism, where is the canonical ring homomorphism R → .

scholarly journals Divisorial Models of Normal Varieties

2017 ◽  
Vol 60 (4) ◽  
pp. 1053-1064 ◽  
Author(s):  
Stefano Urbinati
Keyword(s):  
Toric Varieties ◽  
Finitely Generated ◽  
Normal Varieties ◽  
Canonical Variety ◽  
Canonical Ring

AbstractWe prove that the canonical ring of a canonical variety in the sense of de Fernex and Hacon is finitely generated. We prove that canonical varieties are Kawamata log terminal (klt) if and only if is finitely generated. We introduce a notion of nefness for non-ℚ-Gorenstein varieties and study some of its properties. We then focus on these properties for non-ℚ-Gorenstein toric varieties.

scholarly journals APC2 Cullin Protein and APC11 RING Protein Comprise the Minimal Ubiquitin Ligase Module of the Anaphase-promoting Complex

2001 ◽  
Vol 12 (12) ◽  
pp. 3839-3851 ◽  
Author(s):  
Zhanyun Tang ◽  
Bing Li ◽  
Rajnish Bharadwaj ◽  
Haizhen Zhu ◽  
Engin Özkan ◽  
...  
Keyword(s):  
Ubiquitin Ligase ◽  
Expression System ◽  
Ring Finger ◽  
Cyclin B1 ◽  
Anaphase Promoting Complex ◽  
Ubiquitin Ligase Activity ◽  
Cullin Protein ◽  
Canonical Ring ◽  
Heterodimeric Complex ◽  
Ring Finger Motif

In mitosis, the anaphase-promoting complex (APC) regulates the onset of sister-chromatid separation and exit from mitosis by mediating the ubiquitination and degradation of the securin protein and mitotic cyclins. With the use of a baculoviral expression system, we have reconstituted the ubiquitin ligase activity of human APC. In combination with Ubc4 or UbcH10, a heterodimeric complex of APC2 and APC11 is sufficient to catalyze the ubiquitination of human securin and cyclin B1. However, the minimal APC2/11 ubiquitin ligase module does not possess substrate specificity, because it also ubiquitinates the destruction box deletion mutants of securin and cyclin B1. Both APC11 and UbcH10 bind to the C-terminal cullin homology domain of APC2, whereas Ubc4 interacts with APC11 directly. Zn2+-binding and mutagenesis experiments indicate that APC11 binds Zn2+at a 1:3 M ratio. Unlike the two Zn2+ ions of the canonical RING-finger motif, the third Zn2+ ion of APC11 is not essential for its ligase activity. Surprisingly, with Ubc4 as the E2 enzyme, Zn2+ ions alone are sufficient to catalyze the ubiquitination of cyclin B1. Therefore, the Zn2+ ions of the RING finger family of ubiquitin ligases may be directly involved in catalysis.

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