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 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 Symplectic fillings of lens spaces as Lefschetz fibrations

2016 ◽  
Vol 18 (7) ◽  
pp. 1515-1535 ◽  
Author(s):  
Mohan Bhupal ◽  
Burak Ozbagci
Keyword(s):  
Lens Spaces ◽  
Lefschetz Fibrations

scholarly journals Simplified broken Lefschetz fibrations and trisections of 4-manifolds

2018 ◽  
Vol 115 (43) ◽  
pp. 10894-10900 ◽  
Author(s):  
R. İnanç Baykur ◽  
Osamu Saeki
Keyword(s):  
Lefschetz Fibrations

Shapes of 4D spaces can be studied effectively via maps to standard surfaces. We explain, and illustrate by quintessential examples, how to simplify such generic maps on 4-manifolds topologically, to derive simple decompositions into much better-understood manifold pieces. Our methods not only allow us to produce various interesting families of examples but also to establish a correspondence between simplified broken Lefschetz fibrations and simplified trisections of closed, oriented 4-manifolds.

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 A signature formula for hyperelliptic broken Lefschetz fibrations

2014 ◽  
Vol 173 ◽  
pp. 157-174
Author(s):  
Kenta Hayano ◽  
Masatoshi Sato
Keyword(s):  
Lefschetz Fibrations ◽  
Signature Formula
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