This book, developed from a junior-senior-level course on classical geometries, explores Euclid's Elements alongside modern interpretations. It covers foundational concepts using Hilbert's axioms, the Cartesian plane, and field extensions, culminating in an analysis of non-Euclidean geometries and Platonic solids.
The basic problem of deformation theory in algebraic geometry involves watching a small deformation of one member of a family of objects, such as varieties, or subschemes in a fixed space, or vector bundles on a fixed scheme. In this new book, Robin Hartshorne studies first what happens over small infinitesimal deformations, and then gradually builds up to more global situations, using methods pioneered by Kodaira and Spencer in the complex analytic case, and adapted and expanded in algebraic geometry by Grothendieck. The author includes numerous exercises, as well as important examples illustrating various aspects of the theory. This text is based on a graduate course taught by the author at the University of California, Berkeley.
This book serves as an introduction to abstract algebraic geometry, requiring only knowledge of commutative algebra and basic topology. It features over 400 exercises and three appendices on current research areas, making it suitable for a graduate-level course. Authored by Robin Hartshorne, a notable figure in the field.
InhaltsverzeichnisThe derived category.Application to preschemes.Duality for projective morphisms.Local cohomology.Dualizing complexes and local duality.Residual complexes.The duality theorem.
InhaltsverzeichnisDefinition and elementary properties of the local cohomology groups.Application of local cohomology to preschemes.Relation to depth.Functors on a-modules.Some applications.Local duality.