On real generalized Jacobian varieties

On real generalized Jacobian varieties

In this note, we study effective Cartier divisors with totally real or totally complex supports on a projective curve over R. We give some numerical conditions for an invertible sheaf to be isomorphic or not to such a divisor. We show that these conditions are strongly related to the singularities of the curve and to topological properties of the real part of the Jacobian variety.

Jacobian Varieties

This the original TEX file for my article Jacobian Varieties, published as Chapter VII of Arithmetic geometry (Storrs, Conn., 1984), 167–212, Springer, New York, 1986. The table of contents has been restored, some corrections and minor improvements to the exposition have been made, and an index has been added. The numbering is unchanged.

Group Actions on Jacobian Varieties

Consider a finite groupG acting on a Riemann surface S, and the associated branched Galois cover πG : S → Y = S/G. We introduce the concept of geometric signature for the action of G, and we show that it captures much information: the geometric structure of the lattice of intermediate covers, the isotypical decomposition of the rational representation of the group G acting on the Jacobian varie...

Tautological Cycles on Jacobian Varieties

Q containing C and stable with respect to the Fourier transform, the intersection product, the Pontryagin product, pull-backs and push-forwards of multiplication maps by integers. The tautological ring has a mysterious algebraic structure, which has not been completely understood so far. Only recently Beauville proved that R(C) is finite dimensional as a Q-vector space [Be3]. He proved that the...

On real generalized Ja obian varieties