Algebraic geometry codes over abelian surfaces containing no absolutely irreducible curves of low genus

For an explicit example, let B be a super- singular elliptic curve with all endomorphisms defined, so (c/*. But for most p the quaternion algebra will have non-isomorphic maximal

fixed points of this automorphism of 11 are the points corresponding to hyperelliptic curves. These are known facts in the theory of the Teichmuller space.. The

We prove, using results of SMYTH [S], that if C is an irreducible curve of degree < 2n ifn <^ 7, and <^ 1.7719 n ifn > 7, on a simple principally polarized abelian variety

the minimal multiple of the minimal class which becomes effective on a (general) principally polarized abelian g-fold are also curves of minimal

homogeneous variety X used by Mukai [M] to study the moduli space of K3 surfaces of genus 10.. 0.2).. Recall that homogeneous vector bundles on X are in one to

For two-dimensional abelian varieties a case-by-case examination of the possible decomposition of fA(T) (like in the proof of Lemma 4.2) yields the following:. LEMMA

Further, the Kuga-Satake abelian variety in this case is just a number of copies of the jacobian of the hyper- elliptic curve obtained as the double cover of

The number of principally polarized supersingular abelian surfaces of degenerate type is up to isomorphism equal to h(h + 1 )/2, where h.. is the number of