000			03536nam a22005055i 4500
001			978-3-642-19225-8
003			DE-He213
005			20140220083256.0
007			cr nn 008mamaa
008			111004s2012 gw | s |||| 0|eng d
020			_a9783642192258 _9978-3-642-19225-8
024	7		_a10.1007/978-3-642-19225-8 _2doi
050		4	_aQA564-609
072		7	_aPBMW _2bicssc
072		7	_aMAT012010 _2bisacsh
082	0	4	_a516.35 _223
100	1		_aHolme, Audun. _eauthor.
245	1	2	_aA Royal Road to Algebraic Geometry _h[electronic resource] / _cby Audun Holme.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2012.
300			_aXIV, 366 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aPart 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.
520			_aThis book is about modern algebraic geometry. The title A Royal Road to Algebraic Geometry is inspired by the famous anecdote about the king asking Euclid if there really existed no simpler way for learning geometry, than to read all of his work Elements. 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. From a point of departure in algebraic curves, the exposition moves on to the present shape of the field, culminating with Alexander Grothendieck’s theory of schemes. Contemporary homological tools are explained. The reader will follow a directed path leading up to the main elements of modern algebraic geometry. When the road is completed, the reader is empowered to start navigating in this immense field, and to open up the door to a wonderful field of research. The greatest scientific experience of a lifetime!
650		0	_aMathematics.
650		0	_aGeometry, algebraic.
650		0	_aAlgebra.
650		0	_aGeometry.
650		0	_aAlgebraic topology.
650	1	4	_aMathematics.
650	2	4	_aAlgebraic Geometry.
650	2	4	_aCategory Theory, Homological Algebra.
650	2	4	_aGeometry.
650	2	4	_aAlgebraic Topology.
650	2	4	_aCommutative Rings and Algebras.
650	2	4	_aHistory of Mathematical Sciences.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783642192241
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-642-19225-8
912			_aZDB-2-SMA
999			_c101905 _d101905