Royal Road to Algebraic Geometry

Häftad, Engelska, 2013

AvAudun Holme

909 kr

Beställningsvara. Skickas inom 10-15 vardagar. Fri frakt för medlemmar vid köp för minst 249 kr.

Finns i fler format (1)

Inbunden

1 229 kr

Skickas inom 10-15 vardagar

This book is about modern algebraic geometry. Euclid is said to have answered: “There is no royal road to geometry!” The book starts by explaining this enigmatic answer, the aim of the book being to argue that indeed, in some sense there is a royal road to algebraic geometry.

Produktinformation

Utgivningsdatum2013-11-29
Mått155 x 235 x 20 mm
Vikt546 g
FormatHäftad
SpråkEngelska
Antal sidor366
FörlagSpringer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN9783642429217

Tillhör följande kategorier

Matematik inom Naturvetenskap och teknik
Algebra inom Naturvetenskap och teknik
Topologi inom Naturvetenskap och teknik
Matematikens historia inom Naturvetenskap och teknik

Part I Curves: 1 Affine and Projective Space.- 2 Curves in A2 k and in P2.- 3 Higher Geometry in the Projective Plane.- 4 Plane Curves and Algebra.- 5 Projective Varieties in PNk.- Part II Introduction to Grothendieck’s Theory of Schemes: 6 Categories and Functors.- 7 Constructions and Representable Functors.- 8 Abelian Categories.- 9 The Concept of Spec(A).- 10 The Category of Schemes.- 11 Properties of Morphisms of Schemes.- 12 Modules, Algebras and Bundles on a Scheme.- 13 More Properties of Morphisms, Scheme Theoretic Image and the “Sorite”.- 14 Projective Schemes and Bundles.- 15 Further Properties of Morphisms.- 16 Conormal Sheaf and Projective Bundles.- 17 Cohomology Theory on Schemes.- 18 Intersection Theory.- 19 Characteristic Classes in Algebraic Geometry.- 20 The Riemann-Roch Theorem.- 21 Some Basic constructions in the category of projective kvarieties.- 22 More on Duality.- References.- Index

From the reviews: "The book sets out on a project to convey the big ideas of algebraic geometry in the 21st century in a way that will be accessible and that will get to get to the big ideas (relatively) quickly. ... The topics ... give a good overview of modern algebraic geometry, and I think that a reader who is interested in getting quick statements of theorems will find a lot to like in this book." (Darren Glass, The Mathematical Association of America, August, 2012) "The book under review offers a first introduction to algebraic geometry of a special kind ... . quite a variety of topics from modern algebraic geometry is presented to the reader, often in a sketchy or survey-like manner, but always with hints for further reading. The sections of the single chapters are mostly short, and the presentation is nowhere lengthy or tedious. ... the book must be seen as a charming invitation to algebraic geometry, along some sort of 'royal road' (of pleasure and diversity)." (Werner Kleinert, Zentralblatt MATH, Vol. 1237, 2012)