The Experts below are selected from a list of 803562 Experts worldwide ranked by ideXlab platform
Ana Romero - One of the best experts on this subject based on the ideXlab platform.
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Computing Higher Leray–Serre Spectral Sequences of Towers of Fibrations
Foundations of Computational Mathematics, 2020Co-Authors: Andrea Guidolin, Ana RomeroAbstract:The higher Leray–Serre spectral sequence associated with a tower of Fibrations represents a generalization of the classical Leray–Serre spectral sequence of a Fibration. In this work, we present algorithms to compute higher Leray–Serre spectral sequences leveraging the effective homology technique, which allows to perform computations involving chain complexes of infinite type associated with interesting objects in algebraic topology. In order to develop the programs, implemented as a new module for the Computer Algebra system Kenzo, we translated the original construction of the higher Leray–Serre spectral sequence in a simplicial framework and studied some of its fundamental properties.
David R Morrison - One of the best experts on this subject based on the ideXlab platform.
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f theory on genus one Fibrations
Journal of High Energy Physics, 2014Co-Authors: David R Morrison, Volker BraunAbstract:We argue that M-theory compactified on an arbitrary genus-one Fibration, that is, an elliptic Fibration which need not have a section, always has an Ftheory limit when the area of the genus-one fiber approaches zero. Such genusone Fibrations can be easily constructed as toric hypersurfaces, and various SU(5) × U(1)n and E6 models are presented as examples. To each genus-one Fibration one can associate a τ -function on the base as well as an SL(2,Z) representation which together define the IIB axio-dilaton and 7-brane content of the theory. The set of genus-one Fibrations with the same τ -function and SL(2,Z) representation, known as the Tate-Shafarevich group, supplies an important degree of freedom in the corresponding F-theory model which has not been studied carefully until now. Six-dimensional anomaly cancellation as well as Witten’s zero-mode count on wrapped branes both imply corrections to the usual F-theory dictionary for some of these models. In particular, neutral hypermultiplets which are localized at codimension-two fibers can arise. (All previous known examples of localized hypermultiplets were charged under the gauge group of the theory.) Finally, in the absence of a section some novel monodromies of Kodaira fibers are allowed which lead to new breaking patterns of non-Abelian gauge groups. Email: volker.braun@maths.ox.ac.uk, drm@math.ucsb.edu ar X iv :1 40 1. 78 44 v2 [ he pth ] 2 6 M ar 2 01 4
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f theory on genus one Fibrations
arXiv: High Energy Physics - Theory, 2014Co-Authors: David R Morrison, Volker BraunAbstract:We argue that M-theory compactified on an arbitrary genus-one Fibration, that is, an elliptic Fibration which need not have a section, always has an F-theory limit when the area of the genus-one fiber approaches zero. Such genus-one Fibrations can be easily constructed as toric hypersurfaces, and various $SU(5)\times U(1)^n$ and $E_6$ models are presented as examples. To each genus-one Fibration one can associate a $\tau$-function on the base as well as an $SL(2,\mathbb{Z})$ representation which together define the IIB axio-dilaton and 7-brane content of the theory. The set of genus-one Fibrations with the same $\tau$-function and $SL(2,\mathbb{Z})$ representation, known as the Tate-Shafarevich group, supplies an important degree of freedom in the corresponding F-theory model which has not been studied carefully until now. Six-dimensional anomaly cancellation as well as Witten's zero-mode count on wrapped branes both imply corrections to the usual F-theory dictionary for some of these models. In particular, neutral hypermultiplets which are localized at codimension-two fibers can arise. (All previous known examples of localized hypermultiplets were charged under the gauge group of the theory.) Finally, in the absence of a section some novel monodromies of Kodaira fibers are allowed which lead to new breaking patterns of non-Abelian gauge groups.
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anomalies and the euler characteristic of elliptic calabi yau threefolds
Communications in Number Theory and Physics, 2012Co-Authors: Antonella Grassi, David R MorrisonAbstract:We investigate the delicate interplay between the types of singular fibers in elliptic Fibrations of Calabi-Yau threefolds (used to formulate F-theory) and the "matter" representation of the associated Lie algebra. The main tool is the analysis and the appropriate interpretation of the anomaly formula for six-dimensional supersymmetric theories. We find that this anomaly formula is geometrically captured by a relation among codimension two cycles on the base of the elliptic Fibration, and that this relation holds for elliptic Fibrations of any dimension. We introduce a "Tate cycle" which efficiently describes thisrelation- ship, and which is remarkably easy to calculate explicitly from the Weierstrass equation of the Fibration. We check the anomaly cancellation formula in a num- ber of situations and show how this formula constrains the geometry (and in particular the Euler characteristic) of the Calabi-Yau threefold.
Andrea Guidolin - One of the best experts on this subject based on the ideXlab platform.
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Computing Higher Leray–Serre Spectral Sequences of Towers of Fibrations
Foundations of Computational Mathematics, 2020Co-Authors: Andrea Guidolin, Ana RomeroAbstract:The higher Leray–Serre spectral sequence associated with a tower of Fibrations represents a generalization of the classical Leray–Serre spectral sequence of a Fibration. In this work, we present algorithms to compute higher Leray–Serre spectral sequences leveraging the effective homology technique, which allows to perform computations involving chain complexes of infinite type associated with interesting objects in algebraic topology. In order to develop the programs, implemented as a new module for the Computer Algebra system Kenzo, we translated the original construction of the higher Leray–Serre spectral sequence in a simplicial framework and studied some of its fundamental properties.
Hikaru Yamamoto - One of the best experts on this subject based on the ideXlab platform.
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special lagrangian and deformed hermitian yang mills on tropical manifold
Mathematische Zeitschrift, 2018Co-Authors: Hikaru YamamotoAbstract:From string theory, the notion of deformed Hermitian Yang–Mills connections has been introduced by Marino et al. (J High Energy Phys Paper 5, 2000). After that, Leung et al. (Adv Theor Math Phys 4(6):1319–1341, 2000) proved that it naturally appears as mirror objects of special Lagrangian submanifolds via Fourier–Mukai transform between dual torus Fibrations. In their paper, some conditions are imposed for simplicity. In this paper, data to glue their construction on tropical manifolds are proposed and a generalization of the correspondence is proved without the assumption that the Lagrangian submanifold is a section of the torus Fibration.
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special lagrangian and deformed hermitian yang mills on tropical manifold
arXiv: Differential Geometry, 2017Co-Authors: Hikaru YamamotoAbstract:From string theory, the notion of deformed Hermitian Yang-Mills connections has been introduced by Marino, Minasian, Moore and Strominger. After that, Leung, Yau and Zaslow proved that it naturally appears as mirror objects of special Lagrangian submanifolds via Fourier-Mukai transform between dual torus Fibrations. In their paper, some conditions are imposed for simplicity. In this paper, data to glue their construction on tropical manifolds are proposed and a generalization of the correspondence is proved without the assumption that the Lagrangian submanifold is a section of the torus Fibration.
Sektnan, Lars Martin - One of the best experts on this subject based on the ideXlab platform.
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Moduli theory, stability of Fibrations and optimal symplectic connections
2020Co-Authors: Dervan Ruadhai, Sektnan, Lars MartinAbstract:K-polystability is, on the one hand, conjecturally equivalent to the existence of certain canonical K\"ahler metrics on polarised varieties, and, on the other hand, conjecturally gives the correct notion to form moduli. We introduce a notion of stability for families of K-polystable varieties, extending the classical notion of slope stability of a bundle, viewed as a family of K-polystable varieties via the associated projectivisation. We conjecture that this is the correct condition for forming moduli of Fibrations. Our main result relates this stability condition to K\"ahler geometry: we prove that the existence of an optimal symplectic connection implies semistability of the Fibration. An optimal symplectic connection is a choice of fibrewise constant scalar curvature K\"ahler metric, satisfying a certain geometric partial differential equation. We conjecture that the existence of such a connection is equivalent to polystability of the Fibration. We prove a finite dimensional analogue of this conjecture, by describing a GIT problem for Fibrations embedded in a fixed projective space, and showing that GIT polystability is equivalent to the existence of a zero of a certain moment map.Comment: 44 pages, v2: improved presentation, v3: accepted versio
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Moduli theory, stability of Fibrations and optimal symplectic connections
'Organisation for Economic Co-Operation and Development (OECD)', 2020Co-Authors: Dervan Ruadhai, Sektnan, Lars MartinAbstract:K-polystability is, on the one hand, conjecturally equivalent to the existence of certain canonical Kähler metrics on polarised varieties, and, on the other hand, conjecturally gives the correct notion to form moduli. We introduce a notion of stability for families of K-polystable varieties, extending the classical notion of slope stability of a bundle, viewed as a family of K-polystable varieties via the associated projectivisation. We conjecture that this is the correct condition for forming moduli of Fibrations. Our main result relates this stability condition to Kähler geometry: we prove that the existence of an optimal symplectic connection implies semistability of the Fibration. An optimal symplectic connection is a choice of fibrewise constant scalar curvature Kähler metric, satisfying a certain geometric partial differential equation. We conjecture that the existence of such a connection is equivalent to polystability of the Fibration. We prove a finite dimensional analogue of this conjecture, by describing a GIT problem for Fibrations embedded in a fixed projective space, and showing that GIT polystability is equivalent to the existence of a zero of a certain moment map
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Optimal symplectic connections on holomorphic submersions
2020Co-Authors: Dervan Ruadhai, Sektnan, Lars MartinAbstract:The main result of this paper gives a new construction of extremal K\"ahler metrics on the total space of certain holomorphic submersions, giving a vast generalisation and unification of results of Hong, Fine and others. The principal new ingredient is a novel geometric partial differential equation on such Fibrations, which we call the optimal symplectic connection equation. We begin with a smooth Fibration for which all fibres admit a constant scalar curvature K\"ahler metric. When the fibres admit automorphisms, such metrics are not unique in general, but rather are unique up to the action of the automorphism group of each fibre. We define an equation which, at least conjecturally, determines a canonical choice of constant scalar curvature K\"ahler metric on each fibre. When the Fibration is a projective bundle, this equation specialises to asking that the hermitian metric determining the fibrewise Fubini-Study metric is Hermite-Einstein. Assuming the existence of an optimal symplectic connection, and the existence of an appropriate twisted extremal metric on the base of the Fibration, we show that the total space of the Fibration itself admits an extremal metric for certain polarisations making the fibres small.Comment: 46 pages, published versio
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Optimal Symplectic Connections on Holomorphic Submersions
'Organisation for Economic Co-Operation and Development (OECD)', 2020Co-Authors: Dervan Ruadhai, Sektnan, Lars MartinAbstract:The main result of this paper gives a new construction of extremal Kähler metrics on the total space of certain holomorphic submersions, giving a vast generalisation and unification of results of Hong, Fine and others. The principal new ingredient is a novel geometric partial differential equation on such Fibrations, which we call the optimal symplectic connection equation. We begin with a smooth Fibration for which all fibres admit a constant scalar curvature Kähler metric. When the fibres admit automorphisms, such metrics are not unique in general, but rather are unique up to the action of the automorphism group of each fibre. We define an equation which, at least conjecturally, determines a canonical choice of constant scalar curvature Kähler metric on each fibre. When the Fibration is a projective bundle, this equation specialises to asking that the hermitian metric determining the fibrewise Fubini-Study metric is Hermite-Einstein. Assuming the existence of an optimal symplectic connection, and the existence of an appropriate twisted extremal metric on the base of the Fibration, we show that the total space of the Fibration itself admits an extremal metric for certain polarisations making the fibres small.London Mathematical Society, International Centre for Mathematical Sciences, CIRGE
