000			04973nam a22004933i 4500
001			EBC3040487
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005			20240729124315.0
006			m o d |
007			cr cnu||||||||
008			240724s1996 xx o ||||0 eng d
020			_a9783110811117 _q(electronic bk.)
020			_z9783110150957
035			_a(MiAaPQ)EBC3040487
035			_a(Au-PeEL)EBL3040487
035			_a(CaPaEBR)ebr10588248
035			_a(CaONFJC)MIL558695
035			_a(OCoLC)922943390
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA551 -- .L29 1996eb
082	0		_a516.35
100	1		_aBroglia, Fabrizio.
245	1	0	_aLectures in Real Geometry.
250			_a1st ed.
264		1	_aBerlin/Boston : _bWalter de Gruyter GmbH, _c1996.
264		4	_c©1996.
300			_a1 online resource (282 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aDe Gruyter Expositions in Mathematics Series ; _vv.23
505	0		_aIntro -- Foreword -- Introduction -- Basic algorithms in real algebraic geometry and their complexity: from Sturm's theorem to the existential theory of reals -- 1. Introduction -- 2. Real closed fields -- 2.1. Definition and first examples of real closed fields -- 2.2. Cauchy index and real root counting -- 3. Real root counting -- 3.1. Sylvester sequence -- 3.2. Subresultants and remainders -- 3.3. Sylvester-Habicht sequence -- 3.4. Quadratic forms, Hankel matrices and real roots -- 3.5. Summary and discussion -- 4. Complexity of algorithms -- 5. Sign determinations -- 5.1. Simultaneous inequalities -- 5.2. Thom's lemma and its consequences -- 6. Existential theory of reals -- 6.1. Solving multivariate polynomial systems -- 6.2. Some real algebraic geometry -- 6.3. Finding points on hypersurfaces -- 6.4. Finding non empty sign conditions -- References -- Nash functions and manifolds -- 1. Introduction -- 2. Nash functions -- 3. Approximation Theorem -- 4. Nash manifolds -- 5. Sheaf theory of Nash function germs -- 6. Nash groups -- References -- Approximation theorems in real analytic and algebraic geometry -- Introduction -- I. The analytic case -- 1. The Whitney topology for sections of a sheaf -- 2. A Whitney approximation theorem -- 3. Approximation for sections of a sheaf -- 4. Approximation for sheaf homomorphisms -- II. The algebraic case -- 5. Preliminaries on real algebraic varieties -- 6. A- and B-coherent sheaves -- 7. The approximation theorems in the algebraic case -- III. Algebraic and analytic bundles -- 8. Duality theory -- 9. Strongly algebraic vector bundles -- 10. Approximation for sections of vector bundles -- References -- Real abelian varieties and real algebraic curves -- Introduction -- 1. Generalities on complex tori -- 1.1. Complex tori -- 1.2. Homology and cohomology of tori -- 1.3. Morphisms of complex tori.
505	8		_a1.4. The Albanese and the Picard variety -- 1.5. Line bundles on complex tori -- 1.6. Polarizations -- 1.7. Riemann's bilinear relations and moduli spaces -- 2. Real structures -- 2.1. Definition of real structures -- 2.2. Real models -- 2.3. The action of conjugation on functions and forms -- 2.4. The action of conjugation on cohomology -- 2.5. A theorem of Comessatti -- 2.6. Group cohomology -- 2.7. The action of conjugation on the Albanese variety and the Picard group -- 2.8. Period matrices in pseudonormal form and the Albanese map -- 3. Real abelian varieties -- 3.1. Real structures on complex tori -- 3.2. Equivalence classes for real structures on complex tori -- 3.3. Line bundles on complex tori with a real structure -- 3.4. Riemann bilinear relations for principally polarized real varieties -- 3.5. Moduli spaces of principally polarized real abelian varieties -- 3.6. Real theta functions -- 4. Applications to real curves -- 4.1. The Jacobian of a real curve -- 4.2. Real theta-characteristics -- 4.3. Examples -- 4.4. Moduli spaces and the theorem of Torelli -- 4.5. Singular curves -- References -- Appendix -- Mario Raimondo's contributions to real geometry -- Mario Raimondo's contributions to computer algebra.
520			_aNo detailed description available for "Lectures in Real Geometry".
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aGeometry, Analytic.
650		0	_aGeometry, Algebraic.
655		4	_aElectronic books.
776	0	8	_iPrint version: _aBroglia, Fabrizio _tLectures in Real Geometry _dBerlin/Boston : Walter de Gruyter GmbH,c1996 _z9783110150957
797	2		_aProQuest (Firm)
830		3	_aDe Gruyter Expositions in Mathematics Series
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3040487 _zClick to View
999			_c64175 _d64175