The B-quadrilateral lattice, its transformations and the algebro-geometric construction

摘要

The B-quadrilateral lattice (BQL) provides geometric interpretation of Miwa'sdiscrete BKP equation within the quadrialteral lattice (QL) theory. Afterdiscussing the projective-geometric properties of the lattice we give thealgebro-geometric construction of the BQL ephasizing the role of Prym varietiesand the corresponding theta functions. We also present the reduction of thevectorial fundamental transformation of the QL to the BQL case.