Quaternionic compositum genus

Genus two curves with quaternionic multiplication and modular Jacobian

We describe a method to determine all the isomorphism classes of principal polarizations of the modular abelian surfaces Af with quaternionic multiplication attached to a normalized newform f without complex multiplication. We include an example of Af with quaternionic multiplication for which we find numerically a curve C whose Jacobian is Af up to numerical approximation, and we prove that it...

Compositum of Galois Extensions of Hilbertian Fields

Quaternionic Line-Sets and Quaternionic Kerdock Codes

When n is even, orthogonal spreads in an orthogonal vector space of type O-(2n 2,2) are used to construct line-sets of size (2nm1 + 1)2”-’ in W2”~’ all of whose angles are 90” or cos -1(2-(“-2)/2). These line-sets are then used to obtain quatemionic Kerdock Codes. These constructions are based on ideas used by Calderbank, Cameron, Kantor, and Seidel in real and complex spaces.

On the Compositum of Algebraically Closed Subfields

1. S. Abhyankar, On the ramification of algebraic functions, Amer. J. Math. vol. 77 (1955) pp. 575-592. 2. C. Chevalley, On the theory of local rings, Ann. of Math. vol. 44 (1943), pp. 680-708. 3. -, Introduction to the theory of algebraic functions of one variable, New York, 1951. 4. S. MacLane and O. F. G. Schilling, Zero-dimensional branches of rank one on algebraic varieties, Ann. of Math. ...

Maps to Spaces in the Genus of Infinite Quaternionic Projective Space

Spaces in the genus of infinite quaternionic projective space which admit essential maps from infinite complex projective space are classified. In these cases the sets of homotopy classes of maps are described explicitly. These results strengthen the classical theorem of McGibbon and Rector on maximal torus admissibility for spaces in the genus of infinite quaternionic projective space. An inte...