Seshadri constants and Grassmann bundles over curves

Let $X$ be a smooth complex projective curve, and let $E$ be a vector bundle on $X$ which is not semistable. For a suitably chosen integer $r$, let $\text{Gr}(E)$ be the Grassmann bundle over $X$ that parametrizes the quotients of the fibers of $E$ of dimension $r$. Assuming some numerical conditions on the Harder-Narasimhan filtration of $E$, we study Seshadri constants of ample line bundles on $\text{Gr}(E)$. In many cases, we give the precise value of Seshadri constant. Our results generalize various known results for ${\rm rank}(E)=2$.Comment: Final version; Annales Inst. Fourier (to appear

Parallel algorithms for interactive manipulation of digital terrain models

Interactive three-dimensional graphics applications, such as terrain data representation and manipulation, require extensive arithmetic processing. Massively parallel machines are attractive for this application since they offer high computational rates, and grid connected architectures provide a natural mapping for grid based terrain models. Presented here are algorithms for data movement on the massive parallel processor (MPP) in support of pan and zoom functions over large data grids. It is an extension of earlier work that demonstrated real-time performance of graphics functions on grids that were equal in size to the physical dimensions of the MPP. When the dimensions of a data grid exceed the processing array size, data is packed in the array memory. Windows of the total data grid are interactively selected for processing. Movement of packed data is needed to distribute items across the array for efficient parallel processing. Execution time for data movement was found to exceed that for arithmetic aspects of graphics functions. Performance figures are given for routines written in MPP Pascal