This paper gives a uniform construction of infinitely many primitive Teichmüller curves V ⊂ Mg for g = 2, 3 and 4.

The aim of the paper is twofold. First, some results of Shiota and Plaza-Mart́ın on Prym varieties of curves with an involution are generalized to the general case of an arbitrary automorphism of prime order. Second, the equations defining the moduli space of curves with an automorphism of prime order as a subscheme of the Sato Grassmannian are given.

The aim of the paper is twofold. First, some results of Shiota and Plaza-Mart́ın on Prym varieties of curves with an involution are generalized to the general case of an arbitrary automorphism of prime order. Second, the equations defining the moduli space of curves with an automorphism of prime order as a subscheme of the Sato Grassmannian are given.

The B-quadrilateral lattice (BQL) provides geometric interpretation of Miwa’s discrete BKP equation within the quadrialteral lattice (QL) theory. After discussing the projectivegeometric properties of the lattice we give the algebro-geometric construction of the BQL ephasizing the role of Prym varieties and the corresponding theta functions. We also present the reduction of the vectorial fundam...