A twisted moment map and its equivariance

The Moment Map Revisited

In this paper, we show that the notion of moment map for the Hamiltonian action of a Lie group on a symplectic manifold is a special case of a much more general notion. In particular, we show that one can associate a moment map to a family of Hamiltonian symplectomorphisms, and we prove that its image is characterized, as in the classical case, by a generalized “energy-period” relation.

The Moment Map

Projectivity of Moment Map Quotients

Let G be a complex reductive group acting algebraically on a complex projective variety X . Given a polarisation of X , i.e., an ample G-line bundle L over X , Mumford (see [M-F-K]) defined the notion of stability: A point x ∈ X is said to be semistable with respect to L if and only if there exits m ∈ N and an invariant section s : X → L such that s(x) 6= 0. Let X(L) denote the set of semistabl...

The Moment Map and Equivariant Cohqmology

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Skew-Frobenius map on twisted Edwards curve

In this paper, we consider the Frobenius endomorphism on twisted Edwards curve and give the characteristic polynomial of the map. Applying the Frobenius endomorphism on twisted Edwards curve, we construct a skew-Frobenius map defined on the quadratic twist of an twisted Edwards curve. Our results show that the Frobenius endomorphism on twisted Edwards curve and the skew-Frobenius endomorphism o...