TY  - BOOK
AU  - Patil,Dilip P.
AU  - Storch,Uwe
TI  - Introduction to algebraic geometry and commutative algebra
T2  - IISc lecture note series
SN  - 9789814304566
AV  - QA564 .P385 2010
PY  - 2010///]
CY  - Singapore
PB  - World Scientific
KW  - Geometry, Algebraic
KW  - Commutative algebra
N1  - "ILNS 1"--Spine; Includes bibliographical references (page [199]) and index; -- Chapter 1. Finitely Generated Algebras; -- 1.A. Algebras over a Ring; -- 1.B. Factorization in Rings; -- 1.C. Noetherian Rings and Modules; -- 1.D. Graded Rings and Modules; -- 1.E. Integral Extensions; -- 1.F. Noether's Normalization Lemma and Its Consequences; -- Chapter 2. The K-Spectrum and the Zariski Topology; -- 2.A. The K-Spectrum of a K-Algebra; -- 2.B. Affine Algebraic Sets; -- 2.C. Strong Topology; -- Chapter 3. Prime Spectra and Dimension; -- 3.A. The Prime Spectrum of a Commutative Ring; -- 3.B. Dimension; -- Chapter 4. Schemes; -- 4.A. Sheaves of Rings; -- 4.B. Schemes; -- 4.C. Finiteness Conditions on Schemes; -- 4.D. Product of Schemes; -- 4.E. Affine Morphisms; -- Chapter 5. Projective Schemes; -- 5.A. Projective Schemes; -- 5.B. Main Theorem of Elimination; -- 5.C. Mapping Theorem of Chevalley; -- Chapter 6. Regular, Normal and Smooth Points; -- 6.A. Regular Local Rings; -- 6.B. Normal Domains; -- 6.C. Normalization of a Scheme; -- 6.D. The Module of Kahler Differentials; -- 6.E. Quasi-coherent Sheaves and the Sheaf of Kahler Differentials; -- Chapter 7. Riemann-Roch Theorem; -- 7.A. Coherent Modules on Projective Schemes; -- 7.B. Projective Curves; -- 7.C. The Projective Line; -- 7.D. Riemann-Roch Theorem for General Curves; -- 7.E. Genus of a Projective Curve
N2  - "This introductory textbook for a graduate course in pure mathematics provides a gateway into the two difficult fields of algebraic geometry and commutative algebra. Algebraic geometry, supported fundamentally by commutative algebra, is a cornerstone of pure mathematics; Along the lines developed by Grothendieck, this book delves into the rich interplay between algebraic geometry and commutative algebra. With concise yet clear definitions and synopses a selection is made from the wealth of meterial in the disciplines including the Riemann-Roch theorem for arbitrary projective curves."--pub. desc
ER  -