Closedness of regular $1$-forms on algebraic surfaces

On Closedness of Orbits of Algebraic Groups

Approximation and Closedness of Sectorial Forms

We discuss the question whether the limit form of a sequence of closed, sectorial forms is closed itself. In particular, we prove a convergence theorem from below which assures the limiting form to be closed. As an application of this theorem, we show a different approach to show the closedness of elliptic forms with measurable coefficients. We also give an example of a densely defined, closed,...

ec 1 99 7 REAL ALGEBRAIC SURFACES

The aim of these lectures is to study real algebraic surfaces with the help of the minimal model program. I mainly concentrate on those surfaces F which are rational over C. In some sense this is the class where the theory over C and over R differ the most. The study of real algebraic curves and surfaces is very old, in fact it predates algebraic geometry over C. From our point of view the firs...

Algebraic Geometric Codes on Surfaces

— We study error-correcting codes constructed from projective surfaces over finite fields using the generalized Goppa construction. We obtain bounds for the minimal distance of these codes by understanding how the zero sets of functions on a surface decompose into irreducible components. We also present a decoding algorithm for these codes based on the Luby-Mitzenmacher algorithm for LDPC codes...

Seshadri constants on algebraic surfaces

0. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. Seshadri constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2. Very ample line bundles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3. Bounds on global Seshadri constants . . . . . . . . . . . . . . . . . . . . . . . . 9 4. The degree of sub-maximal cu...