000			03518nam a22004335i 4500
001			978-3-642-20972-7
003			DE-He213
005			20140220083802.0
007			cr nn 008mamaa
008			110824s2011 gw | s |||| 0|eng d
020			_a9783642209727 _9978-3-642-20972-7
024	7		_a10.1007/978-3-642-20972-7 _2doi
050		4	_aQA440-699
072		7	_aPBM _2bicssc
072		7	_aMAT012000 _2bisacsh
082	0	4	_a516 _223
100	1		_aUeberberg, Johannes. _eauthor.
245	1	0	_aFoundations of Incidence Geometry _h[electronic resource] : _bProjective and Polar Spaces / _cby Johannes Ueberberg.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2011.
300			_aXII, 248 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aSpringer Monographs in Mathematics, _x1439-7382
505	0		_aI Projective and Affine Geometries -- 1. Introduction -- 2. Geometries and Pregeometries -- 3. Projective and Affine Planes -- 4. Projective Spaces -- 5. Affine Spaces -- 6. A Characterization of Affine Spaces -- 7. Residues and Diagrams -- 8. Finite geometries -- II Isomorphisms and Collineations -- 1. Introduction -- 2. Morphisms -- 3. Projections -- 4. Collineations of projective and affine spaces -- 5. Central Collineations -- 6. The Theorem of Desargues -- III Projective Geometry over a Vector Space -- 1. Introduction -- 2. The Projective Space P(V) -- 3. Homogeneous Coordinates of Projective Spaces -- 4. Automorphisms of P(V) -- 5. The Affine Space AG(W) -- 6. Automorphisms of A(W) -- 7. The First Fundamental Theorem -- 8. The Second Fundamental Theorem -- IV Polar Spaces and Polarities -- 1. Introduction -- 2. The Theorem of Buekenhout-Shult -- 3. The diagram of a polar space -- 4. Polarities -- 5. Sesquilinear Forms -- 6. Pseudo-quadrics -- 7. The Kleinian Polar Space -- 8. The Theorem of Buekenhout and Parmentier -- V Quadrics and Quadratic Sets -- 1. Introduction -- 2. Quadratic Sets -- 3. Quadrics -- 4. Quadratic Sets in PG(3, K) -- 5. Perspective Quadratic Sets -- 6. Classification of the Quadratic Sets -- 7. The Kleinian Quadric -- 8. The Theorem of Segre -- 9. Further Reading -- References -- Index.
520			_aIncidence geometry is a central part of modern mathematics that has an impressive tradition. The main topics of incidence geometry are projective and affine geometry and, in more recent times, the theory of buildings and polar spaces. Embedded into the modern view of diagram geometry, projective and affine geometry including the fundamental theorems, polar geometry including the Theorem of Buekenhout-Shult and the classification of quadratic sets are presented in this volume. Incidence geometry is developed along the lines of the fascinating work of Jacques Tits and Francis Buekenhout. The book is a clear and comprehensible introduction into a wonderful piece of mathematics. More than 200 figures make even complicated proofs accessible to the reader.
650		0	_aMathematics.
650		0	_aGeometry.
650	1	4	_aMathematics.
650	2	4	_aGeometry.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783642209710
830		0	_aSpringer Monographs in Mathematics, _x1439-7382
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-642-20972-7
912			_aZDB-2-SMA
999			_c107877 _d107877