On line bundles over real algebraic curves

Vector bundles over algebraic curves

On Algebraic Curves over Real Closed Fields. I

In this paper we are concerned with the absolute theory of a smooth irreducible complete algebraic curve X defined over a real closed field K. Our theory is purely algebraic. It may be of interest even in the case that K is the field R of real numbers, since as far as I know there does not exist a purely algebraic theory of curves over R in the literature. Let F denote the field K(X) of rationa...

The line bundles on the moduli of parabolicG - bundles over curves and

Let X be a complex, smooth, complete and connected curve and G be a complex simple and simply connected algebraic group. We compute the Picard group of the stack of quasi-parabolic G-bundles over X, describe explicitly its generators in case for classical G and G 2 and then identify the corresponding spaces of global sections with the vacua spaces of Tsuchiya, Ueno and Yamada. The method uses t...

Line Bundles and Curves on a

Orders on surfaces provided a rich source of examples of noncommutative surfaces. In [HS05] the authors prove the existence of the analogue of the Picard scheme for orders and in [CK11] the Picard scheme is explicitly computed for an order on P ramified on a smooth quartic. In this paper, we continue this line of work, by studying the Picard and Hilbert schemes for an order on P ramified on a u...

Stable Real Algebraic Vector Bundles over a Klein Bottle

Let X be a geometrically connected smooth projective curve of genus one, defined over the field of real numbers, such that X does not have any real points. We classify the isomorphism classes of all stable real algebraic vector bundles over X .