The Experts below are selected from a list of 17049 Experts worldwide ranked by ideXlab platform
Indranil Biswas - One of the best experts on this subject based on the ideXlab platform.
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complex lagrangians in a hyperkaehler manifold and the relative albanese
arXiv: Differential Geometry, 2020Co-Authors: Indranil Biswas, Tomas Gomez, Andre OliveiraAbstract:Let $M$ be the moduli space of complex Lagrangian submanifolds of a hyperK\"ahler manifold $X$, and let $\varpi : \widehat{\mathcal{A}} \rightarrow M$ be the relative Albanese over $M$. We prove that $\widehat{\mathcal{A}}$ has a natural holomorphic Symplectic structure. The projection $\varpi$ defines a completely integrable structure on the Symplectic manifold $\widehat{\mathcal{A}}$. In particular, the fibers of $\varpi$ are complex Lagrangians with respect to the Symplectic Form on $\widehat{\mathcal{A}}$. We also prove analogous results for the relative Picard over $M$.
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on the moduli space of holomorphic g connections on a compact riemann surface
European Journal of Mathematics, 2020Co-Authors: Indranil BiswasAbstract:Let X be a compact connected Riemann surface of genus at least two and G a connected reductive complex affine algebraic group. The Riemann–Hilbert correspondence produces a biholomorphism between the moduli space $${{\mathscr {M}}}_X(G)$$ parametrizing holomorphic G-connections on X and the G-character variety While $${{\mathscr {R}}}(G)$$ is known to be affine, we show that $${{\mathscr {M}}}_X(G)$$ is not affine. The scheme $${{\mathscr {R}}}(G)$$ has an algebraic Symplectic Form constructed by Goldman. We construct an algebraic Symplectic Form on $${{\mathscr {M}}}_X(G)$$ with the property that the Riemann–Hilbert correspondence pulls back the Goldman Symplectic Form to it. Therefore, despite the Riemann–Hilbert correspondence being non-algebraic, the pullback of the Goldman Symplectic Form by the Riemann–Hilbert correspondence nevertheless continues to be algebraic.
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on the moduli space of holomorphic g connections on a compact riemann surface
arXiv: Algebraic Geometry, 2019Co-Authors: Indranil BiswasAbstract:Let $X$ be a compact connected Riemann surface of genus at least two and $G$ a connected reductive complex affine algebraic group. The Riemann--Hilbert correspondence produces a biholomorphism between the moduli space ${\mathcal M}_X(G)$ parametrizing holomorphic $G$--connections on $X$ and the $G$--character variety $${\mathcal R}(G):= \text{Hom}(\pi_1(X, x_0), G)/\!\!/G\, .$$ While ${\mathcal R}(G)$ is known to be affine, we show that ${\mathcal M}_X(G)$ is not affine. The scheme ${\mathcal R}(G)$ has an algebraic Symplectic Form constructed by Goldman. We construct an algebraic Symplectic Form on ${\mathcal M}_X(G)$ with the property that the Riemann--Hilbert correspondence pulls back to the Goldman Symplectic Form to it. Therefore, despite the Riemann--Hilbert correspondence being non-algebraic, the pullback of the Goldman Symplectic Form by the Riemann--Hilbert correspondence nevertheless continues to be algebraic.
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Symplectic Form on hyperpolygon spaces
Geometriae Dedicata, 2015Co-Authors: Indranil Biswas, Carlos Florentino, Leonor Godinho, Alessia MandiniAbstract:In Godinho and Mandini (Adv Math 244:465–532, 2013), a family of parabolic Higgs bundles on \({{\mathbb {C}}}{\mathbb {P}}^1\) was constructed and the parameter space for the family was identified with a moduli space of hyperpolygons. Our aim here is to give a canonical alternative construction of this family. This enables us to compute the Higgs Symplectic Form for this family and show that the isomorphism of Godinho and Mandini (Adv Math 244:465–532, 2013) is actually a symplectomorphism.
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Symplectic Form on hyperpolygon spaces
arXiv: Symplectic Geometry, 2013Co-Authors: Indranil Biswas, Carlos Florentino, Leonor Godinho, Alessia MandiniAbstract:In [GM], a family of parabolic Higgs bundles on $CP^1$ has been constructed and identified with a moduli space of hyperpolygons. Our aim here is to give a canonical alternative construction of this family. This enables us to compute the Higgs Symplectic Form for this family and show that the isomorphism of [GM] is a symplectomorphism.
Gang Tian - One of the best experts on this subject based on the ideXlab platform.
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the singular set of 1 1 integral currents
Annals of Mathematics, 2009Co-Authors: Tristan Riviere, Gang TianAbstract:We prove that 2 dimensional integer multiplicity 2 dimensional rectifiable currents which are almost complex cycles in an almost complex manifold admitting locally a compatible positive Symplectic Form are smooth surfaces aside from isolated points and therefore are J-holomorphic curves.
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the singular set of 1 1 integral currents
arXiv: Analysis of PDEs, 2003Co-Authors: Tristan Riviere, Gang TianAbstract:We prove that 2 dimensional Integral currents (i.e. integer multiplicity 2 dimensional rectifiable currents) which are almost complex cycles in an almost complex manifold admitting locally a compatible Symplectic Form are smooth surfaces aside from isolated points and therefore are J-holomorphic curves.
Simon Hochgerner - One of the best experts on this subject based on the ideXlab platform.
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singular cotangent bundle reduction spin calogero moser systems
Differential Geometry and Its Applications, 2008Co-Authors: Simon HochgernerAbstract:Abstract We develop a bundle picture for singular Symplectic quotients of cotangent bundles acted upon by cotangent lifted actions for the case that the configuration manifold is of single orbit type. Furthermore, we give a Formula for the reduced Symplectic Form in this setting. As an application of this bundle picture we consider Calogero–Moser systems with spin associated to polar representations of compact Lie groups.
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singular cotangent bundle reduction and spin calogero moser systems
arXiv: Symplectic Geometry, 2004Co-Authors: Simon HochgernerAbstract:We develop a bundle picture for the case that the configuration manifold has only a single isotropy type, and give a Formula for the reduced Symplectic Form in this setting. Furthermore, as an application of this bundle picture we consider Calogero-Moser systems with spin associated to polar representations of compact Lie groups.
Mahmut Elbistan - One of the best experts on this subject based on the ideXlab platform.
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a semiclassical Formulation of the chiral magnetic effect and chiral anomaly in even d 1 dimensions
International Journal of Modern Physics A, 2016Co-Authors: Ömer F. Dayi, Mahmut ElbistanAbstract:In terms of the matrix valued Berry gauge field strength for the Weyl Hamiltonian in any even space–time dimensions a Symplectic Form whose elements are matrices in spin indices is introduced. Definition of the volume Form is modified appropriately. A simple method of finding the path integral measure and the chiral current in the presence of external electromagnetic fields is presented. It is shown that within this new approach the chiral magnetic effect as well as the chiral anomaly in even d + 1 dimensions are accomplished straightforwardly.
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The Chiral Magnetic Effect and Chiral Anomaly in 5+1 Dimensions
arXiv: High Energy Physics - Theory, 2014Co-Authors: Ömer F. Dayi, Mahmut ElbistanAbstract:The matrix valued Berry gauge field strength for the Weyl Hamiltonian in 5+1 dimensions is calculated. In terms of it a Symplectic Form whose elements are matrices in spin indices is introduced. Definition of the volume Form is modified appropriately. A simple method of finding the path integral measure and the chiral current in the presence of external electromagnetic fields is presented. It is shown that within this new approach the chiral anomaly as well as the chiral magnetic effect in 5+1 dimensions are accomplished straightforwardly.
Anton Malkin - One of the best experts on this subject based on the ideXlab platform.
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Symplectic structure of the moduli space of flat connection on a riemann surface
Communications in Mathematical Physics, 1995Co-Authors: Yu A Alekseev, Anton MalkinAbstract:We consider the canonical Symplectic structure on the moduli space of flat g-connections on a Riemann surface of genus g with a marked points. For a being a semisimple Lie algebra we obtain an explicit efficient Formula for this Symplectic Form and prove
