Using the Riemann–Hurwitz formula, the hyperelliptic curve with genus g is defined by an equation with degree n = 2 g + 2. Suppose f : X → P 1 is a branched covering with ramification degree 2, where X …

Mar 1, 2023 · We study a class of semistable ordinary hyperelliptic curves over 2-adic fields and the special fibre of their minimal regular model. We show that these curves can be controlled using …

Let X be a hyperelliptic curve over F of genus g ≥ 3 of 2-rank zero, given by an affine equation y2 − y = ∑2g+1 i=1 cixi . We prove that the first slope of the Newton polygon of X is ≥ 1/h.

Question 3.2 asks whether the most rare p-rank, Newton polygon, or Ekedahl-Oort type occurs for the Jacobian of a smooth curve of genus g; here is a natural generalization of that question.

Jan 19, 2001 · Let X be a hyperelliptic curve over F of genus g ≥ 3 of 2-rank zero, given by an affine equation . We prove that the first slope of the Newton polygon of X is ≥ 1/h.

Mar 25, 2026 · A hyperelliptic curve is an algebraic curve given by an equation of the form y^2=f (x), where f (x) is a polynomial of degree n>4 with n distinct roots. If f (x) is a cubic or quartic polynomial, …

Oort [dJO00a] for the Newton polygon strati cation of Ag. As an application, for every prime p, this yields a proof that there exists a supersingular curve of genus