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Non-supersingular hyperelliptic jacobians

Yuri G. Zarhin (2004)

Bulletin de la Société Mathématique de France

Let K be a field of odd characteristic p , let f ( x ) be an irreducible separable polynomial of degree n 5 with big Galois group (the symmetric group or the alternating group). Let C be the hyperelliptic curve y 2 = f ( x ) and J ( C ) its jacobian. We prove that J ( C ) does not have nontrivial endomorphisms over an algebraic closure of K if either n 7 or p 3 .

Normal generation of line bundles on a general k -gonal algebraic curve

Edoardo Ballico, Changho Keem, Seonja Kim (2003)

Bollettino dell'Unione Matematica Italiana

We prove that a very ample special line bundle L of degree d > 3 g - 1 / 2 on a general k -gonal curve is normally generated if the degree of the base locus of its dual bundle K L - 1 does not exceed c k - 2 / 2 , where c := d - 3 g - 1 / 2 .

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