Resolution of Singularities

Description

The notion of singularity is basic to mathematics. In algebraic geometry, the resolution of singularities by simple algebraic mappings is truly a fundamental problem. It has a complete solution in characteristic zero and partial solutions in arbitrary characteristic. The resolution of singularities in characteristic zero is a key result used in many subjects besides algebraic geometry, such as differential equations, dynamical systems, number theory, the theory of $\mathcal{D}$-modules, topology, and mathematical physics. This book is a rigorous, but instructional, look at resolutions. A simplified proof, based on canonical resolutions, is given for characteristic zero. There are several proofs given for resolution of curves and surfaces in characteristic zero and arbitrary characteristic. Besides explaining the tools needed for understanding resolutions, Cutkosky explains the history and ideas, providing valuable insight and intuition for the novice (or expert). There are many examples and exercises throughout the text. The book is suitable for a second course on an exciting topic in algebraic geometry. A core course on resolutions is contained in Chapters 2 through 6. Additional topics are covered in the final chapters. The prerequisite is a course covering the basic notions of schemes and sheaves.

Get the book

Amazon.com

Search the book

eBay.com

Search the book

Other editions

• 

  Resolution of Singularities

  • 186 pages
  • Ebook
  • American Mathematical Soc.

Similar books

• 

  Handbook of Geometry and Topology of Singularities III

  By José Luis Cisneros Molina

  This is the third volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of ...

• 

  Singularities in Algebraic and Analytic Geometry

  By Ruth Ingrid Michler, Caroline Grant Melles

  ... Singularities of Differentiable maps, Volume 1 and 2, Monographs Math., 82-83, Birkhäuser, Boston, 1988. [4] E. Artal-Bartolo, Forme de Seifert des singularités de surface, C. R. Acad. Sci. Paris, t. 313, Série I (1991), 689-692. [5] W ...