GL+(2, ℝ)–orbits in Prym eigenform loci

Cohomological Support Loci for Abel-prym Curves

For an Abel-Prym curve contained in a Prym variety, we determine the cohomological support loci of its twisted ideal sheaves and the dimension of its theta-dual.

FORMAL SYSTEMS EigenForm

Purpose – Discusses the notion of eigenform as explicated by Heinz von Foerster wherein an object is seen to be a token for those behaviors that lend the object its apparent stability in a changing world. Design/methodology/approach – Describes von Foerster’s model for eigenforms and recursions and put this model in the context of mathematical recursions, fractals, set theory, logic, quantum me...

Reflexivity and Eigenform

Dimensions of Prym Varieties

Given a tame Galois branched cover of curves π : X → Y with any finite Galois group G whose representations are rational, we compute the dimension of the (generalized) Prym variety Prymρ(X) corresponding to any irreducible representation ρ of G. This formula can be applied to the study of algebraic integrable systems using Lax pairs, in particular systems associated with Seiberg-Witten theory. ...

Prym Varieties I

is a double covering, where C and C are nonsingular complete curves with Jacobians J and 3. The involution 1: C C interchanging sheets extends to t: I J, and up to some points of order two, 3 splits into an even part J and an odd part P, the Prym variety. The Prym P has a natural polarization on it, but only in two cases where 21 has zero or two branch points do we get a unique principal polari...