scholarly journals On the rationality of quadric surface bundles

2021 ◽  
pp. 1-25
Author(s):  
Matthias Paulsen
Keyword(s):  
Quadric Surface ◽  
Surface Bundles

scholarly journals Stable rationality of quadric surface bundles over surfaces

2018 ◽  
Vol 220 (2) ◽  
pp. 341-365 ◽  
Author(s):  
Brendan Hassett ◽  
Alena Pirutka ◽  
Yuri Tschinkel
Keyword(s):  
Quadric Surface ◽  
Stable Rationality ◽  
Surface Bundles

A Primer on Mapping Class Groups (PMS-49)

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Graduate Students ◽  
Moduli Space ◽  
Riemann Surfaces ◽  
Class Group ◽  
Mapping Class ◽  
Torelli Group ◽  
Surface Bundles ◽  
Surface Homeomorphisms ◽  
Low Dimensional

The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students. It begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn–Nielsen–Baer–theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichmüller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification.

Mathematical Modelling the Process of Cup Wheel Precision Grinding of Rotating Concave Paraboloid

2016 ◽  
Vol 693 ◽  
pp. 837-842
Author(s):  
Fu Yi Xia ◽  
Li Ming Xu ◽  
De Jin Hu
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Abrasive Particle ◽  
Influence Factors ◽  
Machining Process ◽  
Quadric Surface ◽  
Precision Grinding ◽  
Cup Wheel ◽  
The Mathematical Model ◽  
Trajectory Equation

A novel principle of cup wheel grinding of rotating concave quadric surface was proposed. The mathematical model of machining process was established to prove the feasibility of precision grinding of rotating concave paraboloid based on the introduced principle. The conditions of non-interference grinding of concave paraboloid were mathematically derived. The processing range and its influence factors were discussed. The trajectory equation of abrasive particle was concluded. Finally, the math expressions of numerical controlled parameters was put forward in the process of grinding of the concave paraboloid.

INTERSECTING A RAY WITH A QUADRIC SURFACE

1992 ◽  
pp. 275-283 ◽  
Author(s):  
Joseph M. Cychosz ◽  
Warren N. Waggenspack
Keyword(s):  
Quadric Surface

Hand Tracking Using a Quadric Surface Model and Bayesian Filtering

2003 ◽  
pp. 129-141 ◽  
Author(s):  
Roberto Cipolla ◽  
Bjorn Stenger ◽  
Arasanathan Thayananthan ◽  
Philip H. S. Torr
Keyword(s):  
Hand Tracking ◽  
Surface Model ◽  
Bayesian Filtering ◽  
Quadric Surface

scholarly journals K-MODULI OF CURVES ON A QUADRIC SURFACE AND K3 SURFACES

2021 ◽  
pp. 1-41
Author(s):  
KENNETH ASCHER ◽  
KRISTIN DEVLEMING ◽  
YUCHEN LIU
Keyword(s):  
Complete Intersection ◽  
Moduli Space ◽  
Moduli Spaces ◽  
K3 Surfaces ◽  
Moduli Of Curves ◽  
Quadric Surface ◽  
Intersection Curves

Abstract We show that the K-moduli spaces of log Fano pairs $\left(\mathbb {P}^1\times \mathbb {P}^1, cC\right)$ , where C is a $(4,4)$ curve and their wall crossings coincide with the VGIT quotients of $(2,4)$ , complete intersection curves in $\mathbb {P}^3$ . This, together with recent results by Laza and O’Grady, implies that these K-moduli spaces form a natural interpolation between the GIT moduli space of $(4,4)$ curves on $\mathbb {P}^1\times \mathbb {P}^1$ and the Baily–Borel compactification of moduli of quartic hyperelliptic K3 surfaces.

Incidence scrolls

1933 ◽  
Vol 29 (2) ◽  
pp. 235-244
Author(s):  
W. G. Welchman
Keyword(s):  
General Type ◽  
Ruled Surfaces ◽  
Quadric Surface ◽  
General Elliptic

1. The work of this paper was undertaken with a view to finding out what ruled surfaces can be determined by incidences, i.e. generated by the lines which meet a certain set of spaces which I shall call a base. Such ruled surfaces I shall call incidence scrolls. In [3] the lines which meet three lines generate a quadric surface. In [4] it is easy to show that a base consisting of a line and three planes gives the general rational quartic scroll, while the lines which meet five planes in [4] give the general elliptic quintic scroll. One might be tempted to think that at least all the rational normal scrolls could be obtained as incidence scrolls by taking for base a suitable number of spaces containing directrix curves, but unfortunately there is a residual surface except in the case of the rational scrolls of general type and of those with a directrix line.

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