scholarly journals Minimal number of singular fibers in a nonorientable Lefschetz fibration

2022 ◽  
Vol 216 (1) ◽  
Author(s):  
Sinem Onaran ◽  
Burak Ozbagci
Keyword(s):  
Lefschetz Fibration ◽  
Singular Fibers

scholarly journals Minimal number of singular fibers in a Lefschetz fibration

2000 ◽  
Vol 129 (5) ◽  
pp. 1545-1549 ◽  
Author(s):  
Mustafa Korkmaz ◽  
Burak Ozbagci
Keyword(s):  
Lefschetz Fibration ◽  
Singular Fibers

scholarly journals Folding of Hitchin Systems and Crepant Resolutions

2021 ◽  
Author(s):  
Florian Beck ◽  
Ron Donagi ◽  
Katrin Wendland
Keyword(s):  
Fixed Point ◽  
Lie Algebras ◽  
Integrable Systems ◽  
Trace Back ◽  
Dynkin Diagrams ◽  
Or Groups ◽  
Hitchin Systems ◽  
Singular Fibers ◽  
Crepant Resolutions ◽  
Intermediate Jacobian

Abstract Folding of ADE-Dynkin diagrams according to graph automorphisms yields irreducible Dynkin diagrams of $\textrm{ABCDEFG}$-types. This folding procedure allows to trace back the properties of the corresponding simple Lie algebras or groups to those of $\textrm{ADE}$-type. In this article, we implement the techniques of folding by graph automorphisms for Hitchin integrable systems. We show that the fixed point loci of these automorphisms are isomorphic as algebraic integrable systems to the Hitchin systems of the folded groups away from singular fibers. The latter Hitchin systems are isomorphic to the intermediate Jacobian fibrations of Calabi–Yau orbifold stacks constructed by the 1st author. We construct simultaneous crepant resolutions of the associated singular quasi-projective Calabi–Yau three-folds and compare the resulting intermediate Jacobian fibrations to the corresponding Hitchin systems.

scholarly journals K3-FIBERED CALABI–YAU THREEFOLDS II: SINGULAR FIBERS

1999 ◽  
Vol 10 (07) ◽  
pp. 871-896 ◽  
Author(s):  
BRUCE HUNT
Keyword(s):  
Singular Fibers

scholarly journals On the minimal number of singular fibers in Lefschetz fibrations over the torus

2017 ◽  
Vol 145 (8) ◽  
pp. 3607-3616 ◽  
Author(s):  
András I. Stipsicz ◽  
Ki-Heon Yun
Keyword(s):  
Lefschetz Fibrations ◽  
Singular Fibers

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 FIBER PRODUCTS OF ELLIPTIC SURFACES WITH SECTION AND ASSOCIATED KUMMER FIBRATIONS

2009 ◽  
Vol 20 (04) ◽  
pp. 401-426 ◽  
Author(s):  
GRZEGORZ KAPUSTKA ◽  
MICHAŁ KAPUSTKA
Keyword(s):  
Elliptic Surfaces ◽  
Singular Fibers ◽  
Hodge Numbers

We investigate Calabi–Yau three folds which are small resolutions of fiber products of elliptic surfaces with section admitting reduced fibers. We start by the classification of all fibers that can appear on such varieties. Then, we find formulas to compute the Hodge numbers of obtained three folds in terms of the types of singular fibers of the elliptic surfaces. Next, we study Kummer fibrations associated to these fiber products.

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