Singularity Theory I

Arnold, Vladimir I.; Goryunov, V. V.; Lyashko, O. V.; Васильев, Виктор Анатольевич

doi:10.1007/978-3-642-58009-3

Cited by 91 publications

(224 citation statements)

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“…The topology of these manifolds is described by classical singularity theory (see for instance [33] or the more recent [3]). Q n m is homotopy equivalent to a wedge of m spheres of dimension n. The intersection pairing on H n .Q n m / Š Z m is given by if n is odd.…”

Section: Lagrangian Spheresmentioning

confidence: 99%

“…Objects of A mod are bigraded vector spaces M together with maps dC1 M as in (2-2) which have bidegree .1 d; 0/. These should satisfy equations as in (2)(3), where the sum of the two degrees is used in determining all the relevant signs. The bigraded space H r;s .M / has the property that each piece H r; .M / is a graded A-module in the classical sense.…”

Section: Relation To Classical Derived Categoriesmentioning

confidence: 99%

“…1/ i 1 j 2 . These signs come from the chain level realisation of (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12). Namely, take a class OE of bidegree .i; j / on the left hand side of the map, and suppose for simplicity that this is represented by an actual map of chain complexes .…”

Section: Relation To Classical Derived Categoriesmentioning

confidence: 99%

“…Suppose that M satisfies (3)(4)(5), (3)(4)(5)(6). By combining exact triangles (3-3), we arrive at a triangle of the form:…”

Section: Algebraic Definitionmentioning

confidence: 99%

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Lagrangian homology spheres in (A_m) Milnor fibres via ℂ^∗–equivariantA_∞–modules

Seidel

2012

Geom. Topol.

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Section: Lagrangian Spheresmentioning

confidence: 99%

Section: Relation To Classical Derived Categoriesmentioning

confidence: 99%

Section: Relation To Classical Derived Categoriesmentioning

confidence: 99%

“…Suppose that M satisfies (3)(4)(5), (3)(4)(5)(6). By combining exact triangles (3-3), we arrive at a triangle of the form:…”

Section: Algebraic Definitionmentioning

confidence: 99%

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Lagrangian homology spheres in (A_m) Milnor fibres via ℂ^∗–equivariantA_∞–modules

Seidel

2012

Geom. Topol.

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“…[16,17]. For λ 2 ≪ λ 3 ≪ λ 4 ≪ λ n ≤ O(1), they provide a unique solution for which first and second derivatives of the potential vanish along both radial and angular direction in the complex plane: ∂V /∂σ = ∂V /∂σ * = ∂ 2 V /∂σ 2 = ∂ 2 V /∂σ * 2 = 0 (a saddle point condition) [18]. For the first three terms in Eq.…”

mentioning

confidence: 99%

Curvaton Scenario within the Minimal Supersymmetric Standard Model and Predictions for Non-Gaussianity

Mazumdar

Nadathur

2012

Phys. Rev. Lett.

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We provide a model in which both the inflaton and the curvaton are obtained from within the minimal supersymmetric Standard Model, with known gauge and Yukawa interactions. Since now both the inflaton and curvaton fields are successfully embedded within the same sector, their decay products thermalize very quickly before the electroweak scale. This results in two important features of the model: firstly, there will be no residual isocurvature perturbations, and secondly, observable non-Gaussianities can be generated with the non-Gaussianity parameter fNL ∼ O(5 − 1000) being determined solely by the combination of weak-scale physics and the Standard Model Yukawas.The curvaton scenario [1][2][3][4] is an alternative mechanism for the generation of the primordial perturbations whose spectrum is observed in the cosmic microwave background (CMB) [5]. In this scenario, the density perturbations are sourced by the quantum fluctuations of a light scalar field φ, the curvaton, which makes a negligible contribution to the energy density during inflation and decays after the decay of the inflaton field σ. (For a review on inflation including the curvaton mechanism, see [6].) The advantage of the curvaton mechanism is that it can in principle generate measurable non-Gaussianity [1,7]in the primordial density perturbations and also significant residual isocurvature perturbations, neither of which are possible in the usual single-field inflation models. Both signatures are detectable, and if either were to be observed, this would strongly favour the curvaton hypothesis.If the curvaton does not completely dominate the energy density at the time of its decay, the process of conversion of initial isocurvature perturbations into adiabatic curvature perturbations can enhance nonGaussian fluctuations to the level where they might be constrained by the Planck satellite. The enhancement in non-Gaussianity is given by f NL ∼ 5/(4r) for r < 1, where r ≡ ρ φ /ρ rad at the time the curvaton decays [1]. Planck is expected to be able to detect non-Gaussianity of the order f NL 5 [8]. To achieve detectable f NL thus requires small r.However, if either the curvaton or the inflaton belong to a hidden sector beyond the Standard Model (SM), they may decay into other fields beyond the SM degrees of freedom (dof). There is no guarantee that the hidden and visible sector dof should reach thermal equilibrium before Big Bang Nucleosynthesis (BBN) [9] takes place. In this case, residual isocurvature perturbations are expected to be in conflict with CMB data, which constrain them to be less than 10% [5]. If the curvaton belongs to the visible sector but the inflaton does not, a value of r ∼ 1 would avoid this conflict [10] but would render any non-Gaussianity undetectable. Note that if r ∼ 1 the curvaton is solely responsible for exciting all the SM dof so it must carry the SM charges [11,12].For the curvaton model to be observationally distinguishable, we wish the model to be able to create detectable non-Gaussianity. For this, r must be small and bo...

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Singularities of Some Projective Rational Surfaces

Piene

2005

Computational Methods for Algebraic Spline Surfaces

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Singularity Theory I

Cited by 91 publications

References 0 publications

Lagrangian homology spheres in (A_m) Milnor fibres via ℂ^∗–equivariantA_∞–modules

Lagrangian homology spheres in (A_m) Milnor fibres via ℂ^∗–equivariantA_∞–modules

Curvaton Scenario within the Minimal Supersymmetric Standard Model and Predictions for Non-Gaussianity

Singularities of Some Projective Rational Surfaces

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Singularity Theory I

Cited by 91 publications

References 0 publications

Lagrangian homology spheres in (Am) Milnor fibres via ℂ∗–equivariantA∞–modules

Lagrangian homology spheres in (Am) Milnor fibres via ℂ∗–equivariantA∞–modules

Curvaton Scenario within the Minimal Supersymmetric Standard Model and Predictions for Non-Gaussianity

Singularities of Some Projective Rational Surfaces

Contact Info

Product

Resources

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Lagrangian homology spheres in (A_m) Milnor fibres via ℂ^∗–equivariantA_∞–modules

Lagrangian homology spheres in (A_m) Milnor fibres via ℂ^∗–equivariantA_∞–modules