In this paper, we compute the fundamental group of the complement of linear torus curves of maximal contact and we show that it is isomorphic that of generic linear torus curves.

In this paper a construction of quantum codes from self-orthogonal algebraic geometry is provided. Our method based on the CSS as well some peculiar properties underlying curves, named Swiss curves. Several classes well-known curves with many rational points turn out to be Examples are given by Castle GK generalized and Abdon–Bezerra–Quoos maximal Applications our these extends previous one due...

Drasin’s theorem describing meromorphic functions of finite order with maximal sum of deficiencies is extended to holomorphic curves in projective space. A conjecture about holomorphic curves extremal for Cartan’s defect relation is discussed.

We investigate several types of linear codes constructed from two families S̃q and R̃q of maximal curves over finite fields recently constructed by Skabelund as cyclic covers of the Suzuki and Ree curves. Plane models for such curves are provided, and the Weierstrass semigroup H(P ) at an Fq-rational point P is shown to be symmetric.

The formulas for local root numbers of abelian varieties dimension one are known. In this paper we treat the simplest unknown case in two by considering a curve genus 2 defined over 5-adic field such that inertia acts on first $$\ell $$ -adic cohomology group through largest possible finite quotient, isomorphic to $$C_5\rtimes C_8$$ . We give few criteria identify curves and prove formula their...