scholarly journals Boundedness of pluricanonical maps of varieties of general type

2006 ◽  
Vol 166 (1) ◽  
pp. 1-25 ◽  
Author(s):  
Christopher D. Hacon ◽  
James McKernan
Keyword(s):  
General Type ◽  
Pluricanonical Maps

The third and fourth pluricanonical maps of threefolds of general type

2014 ◽  
Vol 157 (2) ◽  
pp. 209-220
Author(s):  
JINSONG XU
Keyword(s):  
General Type ◽  
Complex Numbers ◽  
The Third ◽  
Similar Characterization ◽  
Pluricanonical Maps

AbstractFor a nonsingular projective threefold of general typeXover the field of complex numbers, we show that the fourth pluricanonical map ϕ4is not birational onto its image if and only ifXis birationally fibred by (1,2)-surfaces, provided that vol(X) ≥ 303. We also have similar characterization of birationality of ϕ3.

scholarly journals Pluricanonical systems for 3-folds and 4-folds of general type

2011 ◽  
Vol 152 (1) ◽  
pp. 9-34 ◽  
Author(s):  
LORENZO DI BIAGIO
Keyword(s):  
Lower Bounds ◽  
Large Volume ◽  
General Type ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Canonical Map ◽  
Pluricanonical Maps ◽  
Necessary And Sufficient

AbstractWe explicitly find lower bounds on the volume of threefolds and fourfolds of general type in order to have non-vanishing of pluricanonical systems and birationality of pluricanonical maps. In the case of threefolds of large volume, we also give necessary and sufficient conditions for the fourth canonical map to be birational.

scholarly journals Pluricanonical maps for threefolds of general type

2007 ◽  
Vol 57 (4) ◽  
pp. 1315-1330 ◽  
Author(s):  
Gueorgui Todorov
Keyword(s):  
General Type ◽  
Pluricanonical Maps

Asymptotic behavior of repeated eigenvalues of perturbed self-adjoint elliptic operators

2021 ◽  
pp. 1-16
Author(s):  
Alexander Dabrowski
Keyword(s):  
General Type ◽  
Differential Operators ◽  
Laplacian Operator ◽  
Variational Characterization ◽  
Repeated Eigenvalues ◽  
Direct Extension ◽  
Asymptotic Formulae ◽  
Elliptic Differential Operators ◽  
Domain Perturbations ◽  
Boundary Deformation

A variational characterization for the shift of eigenvalues caused by a general type of perturbation is derived for second order self-adjoint elliptic differential operators. This result allows the direct extension of asymptotic formulae from simple eigenvalues to repeated ones. Some examples of particular interest are presented theoretically and numerically for the Laplacian operator for the following domain perturbations: excision of a small hole, local change of conductivity, small boundary deformation.

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