VARIATION OF TORIC HYPERKÄHLER MANIFOLDS

2003 ◽  
Vol 14 (03) ◽  
pp. 289-311 ◽  
Author(s):  
HIROSHI KONNO
Keyword(s):  
Symplectic Form ◽  
Complex Structure ◽  
Rational Curves ◽  
De Rham Cohomology ◽  
De Rham ◽  
Hyperkähler Manifolds ◽  
Hyperkähler Manifold ◽  
Complex Symplectic ◽  
The Stability ◽  
Two Parameters

A toric hyperKähler manifold is defined to be a smooth hyperKähler quotient of the quaternionic vector space ℍN by a subtorus of TN. It has two parameters corresponding to the de Rham cohomology classes represented by the Kähler form and the complex symplectic form respectively. We study the variation of its complex structure according to these parameters. After the detailed analysis of the stability condition depending on the first parameter, we show that toric hyperKähler manifolds with the same second parameter are related by a sequence of Mukai's elementary transformations. We also give a complete description of its Kähler cone and discuss when certain rational curves exist.

THE DE RHAM COHOMOLOGY OF DIFFERENTIAL SPACES

1989 ◽  
Vol 22 (1) ◽  
pp. 249-272 ◽  
Author(s):  
Wiesław Sasin
Keyword(s):  
De Rham Cohomology ◽  
De Rham ◽  
Differential Spaces

scholarly journals STEENROD OPERATIONS ON THE DE RHAM COHOMOLOGY OF ALGEBRAIC STACKS

2021 ◽  
pp. 1-48
Author(s):  
Federico Scavia
Keyword(s):  
Finite Groups ◽  
Reductive Groups ◽  
Orthogonal Groups ◽  
De Rham Cohomology ◽  
Algebraic Stacks ◽  
Steenrod Operations ◽  
De Rham

Abstract Building upon work of Epstein, May and Drury, we define and investigate the mod p Steenrod operations on the de Rham cohomology of smooth algebraic stacks over a field of characteristic $p>0$ . We then compute the action of the operations on the de Rham cohomology of classifying stacks for finite groups, connected reductive groups for which p is not a torsion prime and (special) orthogonal groups when $p=2$ .

scholarly journals Transverse Hilbert schemes and completely integrable systems

2017 ◽  
Vol 4 (1) ◽  
pp. 263-272 ◽  
Author(s):  
Niccolò Lora Lamia Donin
Keyword(s):  
Integrable Systems ◽  
Hilbert Scheme ◽  
Symplectic Form ◽  
Initial Surface ◽  
Hilbert Schemes ◽  
Completely Integrable Systems ◽  
Completely Integrable ◽  
Symplectic Surface ◽  
Complex Symplectic ◽  
Minimum Polynomial

Abstract In this paper we consider a special class of completely integrable systems that arise as transverse Hilbert schemes of d points of a complex symplectic surface S projecting onto ℂ via a surjective map p which is a submersion outside a discrete subset of S. We explicitly endow the transverse Hilbert scheme Sp[d] with a symplectic form and an endomorphism A of its tangent space with 2-dimensional eigenspaces and such that its characteristic polynomial is the square of its minimum polynomial and show it has the maximal number of commuting Hamiltonians.We then provide the inverse construction, starting from a 2ddimensional holomorphic integrable system W which has an endomorphism A: TW → TW satisfying the above properties and recover our initial surface S with W ≌ Sp[d].

A Statistical Test for the Stability of Covariance Structure

2013 ◽  
Vol 63 (2) ◽  
Author(s):  
Nur Syahidah Yusoff ◽  
Maman Abdurachman Djauhari
Keyword(s):  
Covariance Matrix ◽  
Complex Structure ◽  
Covariance Structure ◽  
Statistical Test ◽  
Dispersion Measure ◽  
Data Sets ◽  
Scalar Representation ◽  
Multivariate Dispersion ◽  
Sample Covariance ◽  
The Stability

The stability of covariance matrix is a major issue in multivariate analysis. As can be seen in the literature, the most popular and widely used tests are Box M-test and Jennrich J-test introduced by Box in 1949 and Jennrich in 1970, respectively. These tests involve determinant of sample covariance matrix as multivariate dispersion measure. Since it is only a scalar representation of a complex structure, it cannot represent the whole structure. On the other hand, they are quite cumbersome to compute when the data sets are of high dimension since they do not only involve the computation of determinant of covariance matrix but also the inversion of a matrix. This motivates us to propose a new statistical test which is computationally more efficient and, if it is used simultaneously with M-test or J-test, we will have a better understanding about the stability of covariance structure. An example will be presented to illustrate its advantage

scholarly journals Cycles in the de Rham cohomology of abelian varieties over number fields

2018 ◽  
Vol 154 (4) ◽  
pp. 850-882
Author(s):  
Yunqing Tang
Keyword(s):  
Endomorphism Ring ◽  
Abelian Varieties ◽  
Number Fields ◽  
De Rham Cohomology ◽  
Tate Conjecture ◽  
De Rham ◽  
Prime Dimension

In his 1982 paper, Ogus defined a class of cycles in the de Rham cohomology of smooth proper varieties over number fields. This notion is a crystalline analogue of$\ell$-adic Tate cycles. In the case of abelian varieties, this class includes all the Hodge cycles by the work of Deligne, Ogus, and Blasius. Ogus predicted that such cycles coincide with Hodge cycles for abelian varieties. In this paper, we confirm Ogus’ prediction for some families of abelian varieties. These families include geometrically simple abelian varieties of prime dimension that have non-trivial endomorphism ring. The proof uses a crystalline analogue of Faltings’ isogeny theorem due to Bost and the known cases of the Mumford–Tate conjecture.

scholarly journals Persistent Liquidity Effects and Long-Run Money Demand

2014 ◽  
Vol 6 (2) ◽  
pp. 71-107 ◽  
Author(s):  
Fernando Alvarez ◽  
Francesco Lippi
Keyword(s):  
Interest Rates ◽  
Money Demand ◽  
Asset Markets ◽  
Propagation Mechanism ◽  
Monetary Model ◽  
Long Run ◽  
Short Run ◽  
The Stability ◽  
Two Parameters

We present a monetary model with segmented asset markets that implies a persistent fall in interest rates after a once-and-for-all increase in liquidity. The gradual propagation mechanism produced by our model is novel in the literature. We provide an analytical characterization of this mechanism, showing that the magnitude of the liquidity effect on impact, and its persistence, depend on the ratio of two parameters: the long-run interest rate elasticity of money demand and the intertemporal substitution elasticity. The model simultaneously explains the short-run “instability” of money demand estimates as well as the stability of long-run interest-elastic money demand. (JEL E13, E31, E41, E43, E52, E62)

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