Movable curves and semistable sheaves

This paper extends a number of known results on slope-semistable sheaves from the classical case to the setting where polarisations are given by movable curve classes. As applications, we obtain new flatness results for reflexive sheaves on singular varieties, as well as a characterisation of finite quotients of Abelian varieties via a Chern class condition.Comment: 24 pages, 2 figures; v2: various minor corrections as requested by referees, will appear in International Mathematics Research Notice

Reflexive differential forms on singular spaces -- Geometry and Cohomology

Based on a recent extension theorem for reflexive differential forms, that is, regular differential forms defined on the smooth locus of a possibly singular variety, we study the geometry and cohomology of sheaves of reflexive differentials. First, we generalise the extension theorem to holomorphic forms on locally algebraic complex spaces. We investigate the (non-)existence of reflexive pluri-differentials on singular rationally connected varieties, using a semistability analysis with respect to movable curve classes. The necessary foundational material concerning this stability notion is developed in an appendix to the paper. Moreover, we prove that Kodaira-Akizuki-Nakano vanishing for sheaves of reflexive differentials holds in certain extreme cases, and that it fails in general. Finally, topological and Hodge-theoretic properties of reflexive differentials are explored.Comment: final version, to appear in Crelle's Journa

Miyaoka-Yau inequalities and the topological characterization of certain klt varieties

Ball quotients, hyperelliptic varieties, and projective spaces are characterized by their Chern classes, as the varieties where the Miyaoka-Yau inequality becomes an equality. Ball quotients, Abelian varieties, and projective spaces are also characterized topologically: if a complex, projective manifold $X$ is homeomorphic to a variety of this type, then $X$ is itself of this type. In this paper, similar results are established for projective varieties with klt singularities that are homeomorphic to singular ball quotients, quotients of Abelian varieties, or projective spaces.Comment: 16 page

Medium Duty Gas-Turbine Engine Blade Removal Tool

Solar Turbines Incorporated sponsored a team of three Cal Poly Undergraduate Mechanical Engineering students to design, manufacture, prototype, and test a tool for the removal of turbine blades from their respective disk assembly without damaging the disk itself. The tool was developed for Solar’s industrial gas turbine engines. The tool complies with all OSHA and Solar Turbines safety and engineering constraints, and was designed for use in a shop facility. The tool was made adaptable for geometric variances in multiple turbine rotor disk stages, and requires no more than one technician to operate using a maximum of two shop resources. The tool stands alone on its own fixture, with ease of portability and disassembly in mind. A discrete process was developed to assist in the transition from the current blade removal process to the new blade removal process. In doing so, future disk damage can be prevented by developing a tool and process used to replace the current rudimentary techniques for blade removal

Evaluation of Geologic CO\u3csub\u3e2\u3c/sub\u3e Sequestration Potential and CO\u3csub\u3e2\u3c/sub\u3e Enhanced Oil Recovery in Kentucky

Kentucky gets approximately 95 percent of its electricity from coal-fired power plants, which produce significant amounts of carbon dioxide (CO2). In 2005, Kentucky coal-fired plants vented 102.8 million short tons of CO2 into the atmosphere. The economic vitality of the state will be affected by its ability to develop and apply a portfolio of technologies that will mitigate input of CO2 into the atmosphere. One technology that has the potential to assist in this challenge is geologic carbon storage, which captures CO2 at point sources and injects it into deep rock strata that can store it for tens of thousands of years and longer. Previous studies suggest that Kentucky has the capacity to store up to 1 billion tons of CO2 in underground strata. By necessity, the capacity calculations are high-level estimates, and consequently, actual capacity remains unproved and even speculative. In addition, other factors such as infrastructure, engineering, and economic and regulatory policy will affect the viability of geologic carbon storage in the state. This report is divided into five chapters, each addressing specific technical aspects pertinent to geologic carbon storage, which is the overarching theme. Chapter 1 is an introduction and overview of geologic carbon storage and the data needed to evaluate its potential. Chapter 2 is a geologic evaluation of the potential to use CO2 for enhanced oil recovery. Chapter 3 is an evaluation of subsurface formation-water geochemistry and implications for CO2 sequestration. Chapter 4 is an evaluation of CO2 storage potential with an emphasis along some of the state\u27s major river corridors. Chapter 5 is a geologic evaluation of CO2 storage potential for nominated coal-to-liquids (gasification) sites