Let $${\mathcal {X}}$$ be an irreducible, non-singular, algebraic curve defined over a field of odd characteristic p. g and $$\gamma $$ the genus p-rank , respectively. The influence on automorphism group $$Aut({\mathcal {X}})$$ is well-known in literature. If $$g \ge 2$$ then finite group, unless so-called Hermitian curve, its order upper bounded by polynomial degree four (Stichtenoth). In 197...

This note pursues the techniques of modified psi classes on the stack of stable maps (cf. [Graber-Kock-Pandharipande]) to give concise solutions to the characteristic number problem of rational curves in P2 or P1×P1 with a cusp or a prescribed triple contact. The classes of such loci are computed in terms of modified psi classes, diagonal classes, and certain codimension-2 boundary classes. Via...

To obtain efficient cryptosystems based on hyperelliptic curves, we studied genus 2 isomorphism classes of hyperelliptic curves in characteristic 2. We found general and optimal form for these curves, just as the short Weierstrass form for elliptic curves. We studied the security and the arithmetic on their jacobian. We also rewrote and optimized the formulas of Lange in characteristic 2, and w...

Distinguishing the stability of characteristic curves for nonlinear resistive circuits is requirement and importance to design various electronic circuit exactly. Since every resistive element has a parasitic component, solutions on the characteristic curves are stable or unstable. In this paper, we show that the stability will be mainly changed at the bifurcation points such as limit point and...