Introduction -- A crash course in commutative algebra -- Ane varieties -- Projective varieties -- Regular and rational maps of quasi projective varieties -- Products -- The blow up of an ideal -- Finite maps of quasi projective varieties -- Dimension of quasi projective algebraic sets -- Zariski's main theorem -- Nonsingularity -- Sheaves -- Applications to regular and rational maps -- Divisors -- Dierential forms and the canonical divisor -- Schemes -- The degree of a projective variety -- Cohomology -- Curves -- An introduction to intersection theory -- Surfaces -- Ramication and etale maps -- Bertini's theorems and general fibers of maps Read more...
Abstract:
Presents a readable and accessible introductory course in algebraic geometry, with most of the fundamental classical results presented with complete proofs. An emphasis is placed on developing connections between geometric and algebraic aspects of the theory. Differences between the theory in characteristic $0$ and positive characteristic are emphasized. Read more...
Author(s): Cutkosky, Steven Dale
Series: Graduate studies in mathematics 188
Publisher: American Mathematical Society
Year: 2018
Language: English
Pages: 498
Tags: Geometry, Algebraic.;Geometry, Algebraic;Geometrische Algebra.;Algebraic geometry -- Instructional exposition (textbooks, tutorial papers, etc.)
Content: A crash course in commutative algebraAffine varietiesProjective varietiesRegular and rational maps of quasi-projective varietiesProductsThe blow-up of an idealFinite maps of quasi-projective varietiesDimension of quasi-projective algebraic setsZariski's main theoremNonsingularitySheavesApplications to regular and rational mapsDivisorsDifferential forms and the canonical divisorSchemesThe degree of a projective varietyCohomologyCurvesAn introduction to intersection theorySurfacesRamification and etale mapsBertini's theorem and general fibers of mapsBibliographyIndex.
