Deformations of Algebraic Schemes

Deformations of Algebraic Schemes
Author: Edoardo Sernesi
Publisher: Springer Science & Business Media
Total Pages: 343
Release: 2007-04-20
Genre: Mathematics
ISBN: 3540306153

This account of deformation theory in classical algebraic geometry over an algebraically closed field presents for the first time some results previously scattered in the literature, with proofs that are relatively little known, yet relevant to algebraic geometers. Many examples are provided. Most of the algebraic results needed are proved. The style of exposition is kept at a level amenable to graduate students with an average background in algebraic geometry.

Geometry and Complex Variables

Geometry and Complex Variables
Author: S. Coen
Publisher: Routledge
Total Pages: 522
Release: 2017-11-22
Genre: Mathematics
ISBN: 1351445278

This reference presents the proceedings of an international meeting on the occasion of theUniversity of Bologna's ninth centennial-highlighting the latest developments in the field ofgeometry and complex variables and new results in the areas of algebraic geometry,differential geometry, and analytic functions of one or several complex variables.Building upon the rich tradition of the University of Bologna's great mathematics teachers, thisvolume contains new studies on the history of mathematics, including the algebraic geometrywork of F. Enriques, B. Levi, and B. Segre ... complex function theory ideas of L. Fantappie,B. Levi, S. Pincherle, and G. Vitali ... series theory and logarithm theory contributions of P.Mengoli and S. Pincherle ... and much more. Additionally, the book lists all the University ofBologna's mathematics professors-from 1860 to 1940-with precise indications of eachcourse year by year.Including survey papers on combinatorics, complex analysis, and complex algebraic geometryinspired by Bologna's mathematicians and current advances, Geometry and ComplexVariables illustrates the classic works and ideas in the field and their influence on today'sresearch.

Deformation Theory

Deformation Theory
Author: Robin Hartshorne
Publisher: Springer Science & Business Media
Total Pages: 241
Release: 2009-11-12
Genre: Mathematics
ISBN: 1441915966

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.

Homotopical Algebraic Geometry II: Geometric Stacks and Applications

Homotopical Algebraic Geometry II: Geometric Stacks and Applications
Author: Bertrand Toën
Publisher: American Mathematical Soc.
Total Pages: 242
Release: 2008
Genre: Mathematics
ISBN: 0821840991

This is the second part of a series of papers called "HAG", devoted to developing the foundations of homotopical algebraic geometry. The authors start by defining and studying generalizations of standard notions of linear algebra in an abstract monoidal model category, such as derivations, étale and smooth morphisms, flat and projective modules, etc. They then use their theory of stacks over model categories to define a general notion of geometric stack over a base symmetric monoidal model category $C$, and prove that this notion satisfies the expected properties.

Topology Conference

Topology Conference
Author: R.F. Dickman
Publisher: Springer
Total Pages: 297
Release: 2006-11-15
Genre: Mathematics
ISBN: 3540379487