Let X be a smooth projective curve of genus g ≥ 2 over the complex numbers. A holomorphic pair on X is a couple (E,φ), where E is a holomorphic bundle over X of rank n and degree d, and φ ∈ H(E) is a holomorphic section. In this paper, we determine the Hodge polynomials of the moduli spaces of rank 2 pairs, using the theory of mixed Hodge structures. We also deal with the case in which E has fi...

A bstract We investigate a relationship between particular class of two-dimensional integrable non-linear σ -models and variations Hodge structures. Concretely, our aim is to study the classical dynamics λ -deformed G / model show that special solutions its equations motion precisely describes one-parameter variation find this obtained by identifying group-valued field -model with Weil operator...