000			03349nam a22004815i 4500
001			978-1-4614-1809-2
003			DE-He213
005			20140220083243.0
007			cr nn 008mamaa
008			120214s2012 xxu| s |||| 0|eng d
020			_a9781461418092 _9978-1-4614-1809-2
024	7		_a10.1007/978-1-4614-1809-2 _2doi
050		4	_aQA564-609
072		7	_aPBMW _2bicssc
072		7	_aMAT012010 _2bisacsh
082	0	4	_a516.35 _223
100	1		_aArapura, Donu. _eauthor.
245	1	0	_aAlgebraic Geometry over the Complex Numbers _h[electronic resource] / _cby Donu Arapura.
264		1	_aBoston, MA : _bSpringer US, _c2012.
300			_aXII, 329p. 17 illus., 1 illus. in color. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aUniversitext, _x0172-5939
505	0		_aPreface -- 1. Plane Curves -- 2. Manifolds and Varieties via Sheaves -- 3. More Sheaf Theory -- 4. Sheaf Cohomology -- 5. de Rham Cohomoloy of Manifolds -- 6. Riemann Surfaces -- 7. Simplicial Methods -- 8. The Hodge Theorem for Riemann Manifolds -- 9. Toward Hodge Theory for Complex Manifolds -- 10. Kahler Manifolds -- 11. A Little Algebraic Surface Theory -- 12. Hodge Structures and Homological Methods -- 13. Topology of Families -- 14. The Hard Lefschez Theorem -- 15. Coherent Sheaves -- 16. Computation of Coherent Sheaves -- 17. Computation of some Hodge numbers -- 18. Deformation Invariance of Hodge Numbers -- 19. Analogies and Conjectures.- References -- Index.
520			_aThis textbook is a strong addition to existing introductory literature on algebraic geometry. The author’s treatment combines the study of algebraic geometry with differential and complex geometry and unifies these subjects using sheaf-theoretic ideas. It is also an ideal text for showing students the connections between algebraic geometry, complex geometry, and topology, and brings the reader close to the forefront of research in Hodge theory and related fields. Unique features of this textbook: - Contains a rapid introduction to complex algebraic geometry - Includes background material on topology, manifold theory and sheaf theory - Analytic and algebraic approaches are developed somewhat in parallel The presentation is easy going, elementary, and well illustrated with examples. “Algebraic Geometry over the Complex Numbers” is intended for graduate level courses in algebraic geometry and related fields. It can be used as a main text for a second semester graduate course in algebraic geometry with emphasis on sheaf theoretical methods or a more advanced graduate course on algebraic geometry and Hodge Theory.
650		0	_aMathematics.
650		0	_aGeometry, algebraic.
650		0	_aDifferential equations, partial.
650		0	_aTopology.
650	1	4	_aMathematics.
650	2	4	_aAlgebraic Geometry.
650	2	4	_aSeveral Complex Variables and Analytic Spaces.
650	2	4	_aTopology.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781461418085
830		0	_aUniversitext, _x0172-5939
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4614-1809-2
912			_aZDB-2-SMA
999			_c101136 _d101136