scholarly journals Explicit Models for Threefolds Fibred by K3 Surfaces of Degree Two

2013 ◽  
Vol 65 (4) ◽  
pp. 905-926
Author(s):  
Alan Thompson
Keyword(s):  
K3 Surfaces ◽  
Canonical Model ◽  
Log Canonical ◽  
Small Set

AbstractWe consider threefolds that admit a fibration by K3 surfaces over a nonsingular curve, equipped with a divisorial sheaf that defines a polarization of degree two on the general fibre. Under certain assumptions on the threefold we show that its relative log canonical model exists and can be explicitly reconstructed from a small set of data determined by the original fibration. Finally, we prove a converse to this statement: under certain assumptions, any such set of data determines a threefold that arises as the relative log canonical model of a threefold admitting a fibration by K3 surfaces of degree two.

scholarly journals The final log canonical model ofℳ6

2014 ◽  
Vol 8 (5) ◽  
pp. 1113-1126 ◽  
Author(s):  
Fabian Müller
Keyword(s):  
Canonical Model ◽  
Log Canonical

scholarly journals Hyperbolicity for Log Smooth Families with Maximal Variation

2021 ◽  
Author(s):  
Chuanhao Wei ◽  
Lei Wu
Keyword(s):  
Open Subset ◽  
Minimal Model ◽  
General Type ◽  
Canonical Model ◽  
Base Space ◽  
Zariski Open Subset ◽  
Smooth Family ◽  
Log Canonical ◽  
The Family

Abstract We prove that the base space of a log smooth family of log canonical pairs of log general type is of log general type as well as algebraically degenerate, when the family admits a relative good minimal model over a Zariski open subset of the base and the relative log canonical model is of maximal variation.

scholarly journals The Newton tree: geometric interpretation and applications to the motivic zeta function and the log canonical threshold

2015 ◽  
Vol 159 (3) ◽  
pp. 481-515 ◽  
Author(s):  
PIERRETTE CASSOU-NOGUÈS ◽  
WILLEM VEYS
Keyword(s):  
Zeta Function ◽  
Newton Polygon ◽  
Geometric Interpretation ◽  
Canonical Model ◽  
Newton Polygons ◽  
Log Canonical Threshold ◽  
Newton Algorithm ◽  
Log Canonical ◽  
Motivic Zeta Function ◽  
The Ideal

AbstractLet${\mathcal I}$be an arbitrary ideal in${\mathbb C}$[[x,y]]. We use the Newton algorithm to compute by induction the motivic zeta function of the ideal, yielding only few poles, associated to the faces of the successive Newton polygons. We associate a minimal Newton tree to${\mathcal I}$, related to using good coordinates in the Newton algorithm, and show that it has a conceptual geometric interpretation in terms of the log canonical model of${\mathcal I}$. We also compute the log canonical threshold from a Newton polygon and strengthen Corti's inequalities.

scholarly journals On finiteness of log canonical models

2022 ◽  
Author(s):  
Zhan Li
Keyword(s):  
Convex Set ◽  
Canonical Model ◽  
Canonical Models ◽  
Log Canonical ◽  
Rational Polytope

Let [Formula: see text] be klt pairs with [Formula: see text] a convex set of divisors. Assuming that the relative Kodaira dimensions of such pairs are non-negative, then there are only finitely many log canonical models when the boundary divisors vary in a rational polytope in [Formula: see text]. As a consequence, we show the existence of the log canonical model for a klt pair [Formula: see text] with real coefficients.

Arrangement Of Monomeric Units In Fibrin

1979 ◽  
Author(s):  
Jan Hermans
Keyword(s):  
Fiber Axis ◽  
High Symmetry ◽  
Linear Polymers ◽  
Fiber Volume ◽  
High Fiber ◽  
Rotation Axes ◽  
Small Set ◽  
Helical Turn ◽  
The One ◽  
Kinetics Of

Measurements of light scattering have given much information about formation and properties of fibrin. These studies have determined mass-length ratio of linear polymers (protofibrils) and of fibers, kinetics of polymerization and of lateral association and volume-mass ratio of thick fibers. This ratio is 5 to 1. On the one hand, this high value suggests that the fiber contains channels that allow the diffusion of enzymes such as Factor XHIa and plasmin; on the other hand, the high value appears paradoxical for a stiff fiber made up of elongated units (fibrin monomers) arranged in parallel. Such a high fiber volume is a property of only a small set out of many high-symmetry models of fibrin, which may be constructed from overlapping three-domain monomers which are arranged into strands, are aligned nearly parallel to the fiber axis and make adequate longitudinal and lateral contacts. These models contain helical protofibrils related to each other by rotation axes parallel to the fiber axis. The protofibrils may contain 2, 3 or 4 monomers per helical turn and there are four possible symmetries. A large specific volume is achieved if the ends of each monomer are slightly displaced from the protofibril axis, either by a shift or by a tilt of the monomer. The fiber containing tilted monomers is more highly interconnected; the two ends of a tilted monomer form lateral contacts with different adjacent protofibrils, whereas the two ends of a non-tilted monomer contact the same adjacent protofibril(s).

A canonical model of migration to cities

1985 ◽  
Vol 3 (1) ◽  
pp. 54-61
Author(s):  
Shekhar Mukherji
Keyword(s):  
Canonical Model

scholarly journals Motivic integral of K3 surfaces over a non-archimedean field

2011 ◽  
Vol 228 (5) ◽  
pp. 2688-2730 ◽  
Author(s):  
Allen J. Stewart ◽  
Vadim Vologodsky
Keyword(s):  
K3 Surfaces
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