Algorithm for determining the type of a singular fiber in an elliptic pencil

1975 ◽  
pp. 33-52 ◽  
Author(s):  
J. Tate
Keyword(s):  
Singular Fiber ◽  
Elliptic Pencil

scholarly journals Quantum Computing, Seifert Surfaces, and Singular Fibers

2019 ◽  
Vol 1 (1) ◽  
pp. 12-22 ◽  
Author(s):  
Michel Planat ◽  
Raymond Aschheim ◽  
Marcelo M. Amaral ◽  
Klee Irwin
Keyword(s):  
Quantum Computing ◽  
Quantum Computer ◽  
Complete Information ◽  
Singular Fiber ◽  
Dynkin Diagrams ◽  
Singular Fibers ◽  
Seifert Surfaces ◽  
Trefoil Knot ◽  
Universal Quantum

The fundamental group π 1 ( L ) of a knot or link L may be used to generate magic states appropriate for performing universal quantum computation and simultaneously for retrieving complete information about the processed quantum states. In this paper, one defines braids whose closure is the L of such a quantum computer model and computes their braid-induced Seifert surfaces and the corresponding Alexander polynomial. In particular, some d-fold coverings of the trefoil knot, with d = 3 , 4, 6, or 12, define appropriate links L, and the latter two cases connect to the Dynkin diagrams of E 6 and D 4 , respectively. In this new context, one finds that this correspondence continues with Kodaira’s classification of elliptic singular fibers. The Seifert fibered toroidal manifold Σ ′ , at the boundary of the singular fiber E 8 ˜ , allows possible models of quantum computing.

scholarly journals Splittability of Stellar Singular Fiber with Three Branches

2006 ◽  
Vol 29 (1) ◽  
pp. 1-17
Author(s):  
Kazushi Ahara ◽  
Shigeru Takamura
Keyword(s):  
Singular Fiber

scholarly journals A Topological Approach to Indices of Geometric Operators on Manifolds with Fibered Boundaries

2019 ◽  
Vol 377 (1) ◽  
pp. 77-147
Author(s):  
Mayuko Yamashita
Keyword(s):  
Fiber Bundles ◽  
Localization Problem ◽  
Topological Approach ◽  
Singular Fiber

Abstract In this paper, we investigate topological aspects of indices of twisted geometric operators on manifolds equipped with fibered boundaries. We define K-groups relative to the pushforward for boundary fibration, and show that indices of twisted geometric operators, defined by complete $$\Phi $$Φ or edge metrics, can be regarded as the index pairing over these K-groups. We also prove various properties of these indices using groupoid deformation techniques. Using these properties, we give an application to the localization problem of signature operators for singular fiber bundles.

scholarly journals ­Comparative spigot ontogeny across the spider tree of life

PeerJ ◽  
2018 ◽  
Vol 6 ◽  
pp. e4233 ◽  
Author(s):  
Rachael E. Alfaro ◽  
Charles E. Griswold ◽  
Kelly B. Miller
Keyword(s):  
Phylogenetic Signal ◽  
Correlation Coefficients ◽  
Generalized Least Squares ◽  
Tree Of Life ◽  
Morphological Data ◽  
Singular Fiber ◽  
Rigorous Testing ◽  
Ancestral Character Estimation ◽  
First Time ◽  
Hogna Carolinensis

Spiders are well known for their silk and its varying use across taxa. Very few studies have examined the silk spigot ontogeny of the entire spinning field of a spider. Historically the spider phylogeny was based on morphological data and behavioral data associated with silk. Recent phylogenomics studies have shifted major paradigms in our understanding of silk use evolution, reordering phylogenetic relationships that were once thought to be monophyletic. Considering this, we explored spigot ontogeny in 22 species, including Dolomedes tenebrosus and Hogna carolinensis, reported here for the first time. This is the first study of its kind and the first to incorporate the Araneae Tree of Life. After rigorous testing for phylogenetic signal and model fit, we performed 60 phylogenetic generalized least squares analyses on adult female and second instar spigot morphology. Six analyses had significant correlation coefficients, suggesting that instar, strategy, and spigot variety are good predictors of spigot number in spiders, after correcting for bias of shared evolutionary history. We performed ancestral character estimation of singular, fiber producing spigots on the posterior lateral spinneret whose potential homology has long been debated. We found that the ancestral root of our phylogram of 22 species, with the addition of five additional cribellate and ecribellate lineages, was more likely to have either none or a modified spigot rather than a pseudoflagelliform gland spigot or a flagelliform spigot. This spigot ontogeny approach is novel and we can build on our efforts from this study by growing the dataset to include deeper taxon sampling and working towards the capability to incorporate full ontogeny in the analysis.

Pseudo-Abelian varieties

1954 ◽  
Vol 50 (3) ◽  
pp. 360-371 ◽  
Author(s):  
L. Roth
Keyword(s):  
Abelian Varieties ◽  
Intersection Number ◽  
Elliptic Surface ◽  
Continuous Group ◽  
Groups Of Automorphisms ◽  
Elliptic Pencil ◽  
Hyperelliptic Surface ◽  
Important Character ◽  
Branch Curve

It is a familiar fact that the Picard surface (or hyperelliptic surface of rank 1) admits a completely transitive permutable continuous group of ∞2 automorphisms. There are, however, other non-scrollar surfaces which possess continuous groups of automorphisms, namely, the elhptic surfaces. Every elliptic surface V2 contains a pencil of birationally equivalent elhptic curves, which are the trajectories of the group in question; it also contains a second, elliptic, pencil of birationally equivalent curves; the intersection number of the two pencils is an important character, known as the determinant of V2. Just as any Picard surface can be mapped on a multiple Picard surface of divisor unity, so V2 can be mapped on a multiple elliptic surface of determinant unity, the branch curve (if any) corresponding to a certain number of trajectories.

Sign in / Sign up

Export Citation Format

Share Document