According to Mukai, any prime Fano threefold X of genus 7 is a linear section of the spinor tenfold in the projectivized half-spinor space of Spin(10). The orthogonal linear section of the spinor tenfold is a canonical genus-7 curve Γ, and the intermediate Jacobian J(X) is isomorphic to the Jacobian of Γ. It is proven that, for a generic X , the Abel-Jacobi map of the family of elliptic sextics...

This paper proposes a novel scheme of group key management based on Jacobian Elliptic Chebyshev Rational Map, named Jacobian Group Key Management(JGKM). The scheme is more efficient than other group key managements since fewer re-keying messages are sent when group membership changes. Besides, it provides both forward and backward secrecy. Therefore, this proposal is helpful to deploy secure mu...

We consider the map from conductivities to the response matrix. For critical circular planar graphs, this map is known to be invertible, at least when the conductivities are positive. We calculate the Jacobian determinant of this map, which turns out to have a fairly simple form. Using this we show that for arbitrary critical circular planar networks, the map from conductivities to the response...

It is shown that a polynomial map F = (P, Q) of C with finite fibres is a polynomial automorphism if for all (a : b) ∈ P the polynomials aP + bQ are irreducible and the curves aP + bQ = 0 are rational curves. In consequence, a non-zero constant Jacobian polynomial map F of C is a polynomial automorphism if the inverse images F(l) of complex lines l ⊂ C passing through (0, 0) are irreducible rat...

Sergey Pinchuk discovered a class of pairs of real polynomials in two variables that have a nowhere vanishing Jacobian determinant and define maps of the real plane to itself that are not one-to-one. This paper describes the asymptotic behavior of one specific map in that class. The level of detail presented permits a good geometric visualization of the map. Errors in an earlier description of ...

Real hyperelliptic curves admit two structures suitable for cryptography — the Jacobian (a finite abelian group) and the infrastructure. Mireles Morales described precisely the relationship between these two structures, and made the assertion that when implemented with balanced divisor arithmetic, the Jacobian generically yields more efficient arithmetic than the infrastructure for cryptographi...

In this article we consider the spaces H(X) parametrizing curves of degree d and genus g on a smooth cubic threefold X ⊂ P, with regard in particular to the Abel-Jacobi map ud : H(X) → J(X) to the intermediate Jacobian J(X) of X . Our principle result is that for all d ≤ 5 the map ud coincides with the maximal rationally connected fibration of H(X).

On a closed symplectic surface Σ of genus two or more, we give a new construction of an extended flux map (a crossed homomorphism from the symplectomorphism group Symp(Σ) to the cohomology group H(Σ;R) that extends the flux homomorphism). This construction uses the topology of the Jacobian of the surface and a correction factor related to the Johnson homomorphism. For surfaces of genus three or...

Jacobians of degenerating families curves are well-understood over 1-dimensional bases due to work Néron and Raynaud; the fundamental tool is model its description via Picard functor. Over higher-dimensional models typically do not exist, but in this paper we construct a universal base change ? ˜ g,n ?? ¯ after which N /? jacobian does exist. This yields new partial compactification moduli spac...

Using a new key management system and Jacobian elliptic map, speech encryption scheme has been developed for secure communication data. map-based as novel method to improve the existing methods' drawbacks, such poor quality in decrypted signals, residual intelligibility, high computational complexity, low-key space. map solution, cryptosystem was created. The proposed scheme's performance is ev...