The Experts below are selected from a list of 267 Experts worldwide ranked by ideXlab platform
Dragos Oprea - One of the best experts on this subject based on the ideXlab platform.
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Rationality of descendent series for Hilbert and Quot schemes of surfaces
arXiv: Algebraic Geometry, 2020Co-Authors: Drew Johnson, Dragos Oprea, Rahul PandharipandeAbstract:Quot schemes of quotients of a Trivial Bundle of arbitrary rank on a nonsingular projective surface X carry perfect obstruction theories and virtual fundamental classes whenever the quotient sheaf has at most 1-dimensional support. The associated generating series of virtual Euler characteristics was conjectured to be a rational function when X is simply connected. We conjecture here the rationality of more general descendent series with insertions obtained from the Chern characters of the tautological sheaf. We prove the rationality of descendent series in Hilbert scheme cases for all curve classes and in Quot scheme cases when the curve class is 0.
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Virtual intersections on the Quot scheme and Vafa-Intriligator formulas
Duke Mathematical Journal, 2007Co-Authors: Alina Marian, Dragos OpreaAbstract:We construct a virtual fundamental class on the Quot scheme parametrizing quotients of a Trivial Bundle on a smooth projective curve. We use the virtual localization formula to calculate virtual intersection numbers on Quot. As a consequence, we re-prove the Vafa-Intriligator formula; our answer is valid even when the Quot scheme is badly behaved. More intersections of Vafa-Intriligator type are computed by the same method. Finally, we present an application to the nonvanishing of the Pontryagin ring of the moduli space of Bundles
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Virtual intersections on the Quot-scheme and Vafa-Intriligator formulas
arXiv: Algebraic Geometry, 2005Co-Authors: Alina Marian, Dragos OpreaAbstract:We construct a virtual fundamental class on the Quot scheme parametrizing quotients of a Trivial Bundle on a curve. We use the virtual localization formula to calculate virtual intersection numbers on Quot. As a consequence, we reprove the Vafa-Intriligator formula; our answer is valid even when the Quot scheme is badly behaved. More intersections are computed by the same method. Finally, we present an application to the non-vanishing of the Pontrjagin ring of the moduli space of Bundles.
David González-Álvaro - One of the best experts on this subject based on the ideXlab platform.
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Nonnegative curvature on stable Bundles over compact rank one symmetric spaces
Advances in Mathematics, 2017Co-Authors: David González-ÁlvaroAbstract:Abstract In this note we show that every (real or complex) vector Bundle over a compact rank one symmetric space carries, after taking the Whitney sum with a Trivial Bundle of sufficiently large rank, a metric with nonnegative sectional curvature. We also examine the case of complex vector Bundles over other manifolds, and give upper bounds for the rank of the Trivial Bundle that is necessary to add when the base is a sphere.
Alina Marian - One of the best experts on this subject based on the ideXlab platform.
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Virtual intersections on the Quot scheme and Vafa-Intriligator formulas
Duke Mathematical Journal, 2007Co-Authors: Alina Marian, Dragos OpreaAbstract:We construct a virtual fundamental class on the Quot scheme parametrizing quotients of a Trivial Bundle on a smooth projective curve. We use the virtual localization formula to calculate virtual intersection numbers on Quot. As a consequence, we re-prove the Vafa-Intriligator formula; our answer is valid even when the Quot scheme is badly behaved. More intersections of Vafa-Intriligator type are computed by the same method. Finally, we present an application to the nonvanishing of the Pontryagin ring of the moduli space of Bundles
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Virtual intersections on the Quot-scheme and Vafa-Intriligator formulas
arXiv: Algebraic Geometry, 2005Co-Authors: Alina Marian, Dragos OpreaAbstract:We construct a virtual fundamental class on the Quot scheme parametrizing quotients of a Trivial Bundle on a curve. We use the virtual localization formula to calculate virtual intersection numbers on Quot. As a consequence, we reprove the Vafa-Intriligator formula; our answer is valid even when the Quot scheme is badly behaved. More intersections are computed by the same method. Finally, we present an application to the non-vanishing of the Pontrjagin ring of the moduli space of Bundles.
Hasan Gumral - One of the best experts on this subject based on the ideXlab platform.
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geometry ofplasma dynamics ii lie algebra of hamiltonian vector fields
The Journal of Geometric Mechanics, 2012Co-Authors: Oǧul Esen, Hasan GumralAbstract:We introduce natural differential geometric structures underlying the Poisson-Vlasov equations in momentum variables. First, we decompose the space of all vector fields over particle phase space into a semi-direct product algebra of Hamiltonian vector fields and its complement. The latter is related to dual space of the Lie algebra. We identify generators of homotheties as dynamically irrelevant vector fields in the complement. Lie algebra of Hamiltonian vector fields is isomorphic to the space of all Lagrangian submanifolds with respect to Tulczyjew symplectic structure. This is obtained as tangent space at the identity of the group of canonical diffeomorphisms represented as space of sections of a Trivial Bundle. We obtain the momentum-Vlasov equations as vertical equivalence, or representative, of complete cotangent lift of Hamiltonian vector field generating particle motion. Vertical representatives can be described by holonomic lift from a Whitney product to a Tulczyjew symplectic space. We show that vertical representatives of complete cotangent lifts form an integrable subBundle of this Tulczyjew space. We exhibit dynamical relations between Lie algebras of Hamiltonian vector fields and of contact vector fields, in particular; infinitesimal quantomorphisms on quantization Bundle. Gauge symmetries of particle motion are extended to tensorial objects including complete lift of particle motion. Poisson equation is then obtained as zero value of momentum map for the Hamiltonian action of gauge symmetries for kinematical description.
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Lie Algebra of Hamiltonian Vector Fields and the Poisson-Vlasov Equations
arXiv: Mathematical Physics, 2012Co-Authors: Oğul Esen, Hasan GumralAbstract:We introduce natural differential geometric structures underly- ing the Poisson-Vlasov equations in momentum variables. First, we decompose the space of all vector fields over particle phase space into a semi-direct product algebra of Hamiltonian vector fields and its complement. The latter is related to dual space of the Lie algebra. We identify generators of homotheties as dynam- ically irrelevant vector fields in the complement. Lie algebra of Hamiltonian vector fields is isomorphic to the space of all Lagrangian submanifolds with respect to Tulczyjew symplectic structure. This is obtained as tangent space at the identity of the group of canonical diffeomorphisms represented as space of sections of a Trivial Bundle. We obtain the momentum-Vlasov equations as vertical equivalence, or representative, of complete cotangent lift of Hamilto- nian vector field generating particle motion. Vertical representatives can be described by holonomic lift from a Whitney product to a Tulczyjew symplectic space. We show that vertical representatives of complete cotangent lifts form an integrable subBundle of this Tulczyjew space. A generalization of complete cotangent lift is obtained by a Lie algebra homomorphism from the algebra of symmetric contravariant tensor fields with Schouten concomitant to the Lie al- gebra of Hamiltonian vector fields. Momentum maps for particular subalgebras of symmetric contravariant tensors result in plasma-to-fluid map in momen- tum variables of Vlasov equations. We exhibit dynamical relations between Lie algebras of Hamiltonian vector fields and of contact vector fields, in particu- lar; infinitesimal quantomorphisms on their quantization Bundle. A diagram connecting these kinetic and fluid theories is presented. Gauge symmetries of particle motion are extended to tensorial objects including complete lift of par- ticle motion. Poisson equation is then obtained as zero value of momentum map for the Hamiltonian action of gauge symmetries for kinematical description. 1This is an expanded (with the additions of more remarks and, sections 4 and 5.4) version of the article "Geometry of plasma dynamics II: Lie algebra of Hamiltonian vector fields" to appear in Journal of Geometric Mechanics, 2012.
A. Leibman - One of the best experts on this subject based on the ideXlab platform.
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Some monodromy representations of generalized braid groups
Communications in Mathematical Physics, 1994Co-Authors: A. LeibmanAbstract:A flat connection on the Trivial Bundle over the complement inC n of the complexification of the system of the reflecting hyperplanes of theB n,D n Coxeter groups is built from a simple Lie algebra and its representation. The corresponding monodromy representations of the generalized braid groupsXB n,XD n are computed in the simplest case.
