Classical algebraic geometry : a modern view / Igor V. Dolgachev

By:

Dolgachev, Igor V, 1944- [aut]

Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Publisher: Cambridge ; New York : Cambridge University Press, 2012Edition: Online-AusgDescription: Online-Ressource (1 online resource (xii, 639 p.))ISBN:

9781283610582
1283610582
9781139550871

Subject(s):

Additional physical formats: 9781107017658 | 1283609711 | Druckausg.: Classical algebraic geometry. 1. publ. Cambridge [u.a.] : Cambridge University Press, 2012. XII, 639 S.MSC: MSC: *14-02 | 14H50 | 14J25 | 14E07 | 14H42 | 14Mxx | 14N15 | 14N25 | 14-01 | 14NxxRVK: RVK: SK 380LOC classification:

QA564

Online resources:

Zugang im Netz des KIT

Summary: This detailed exposition makes classical algebraic geometry accessible to the modern mathematician.Summary: Cover -- Classical Algebraic Geometry -- Title -- Copyright -- Dedication -- Contents -- Preface -- 1 Polarity -- 1.1 Polar hypersurfaces -- 1.1.1 The polar pairing -- 1.1.2 First polars -- 1.1.3 Polar quadrics -- 1.1.4 The Hessian hypersurface -- 1.1.5 Parabolic points -- 1.1.6 The Steinerian hypersurface -- 1.1.7 The Jacobian hypersurface -- 1.2 The dual hypersurface -- 1.2.1 The polar map -- 1.2.2 Dual varieties -- 1.3 Polar s-hedra -- 1.3.1 Apolar schemes -- 1.3.2 Sums of powers -- 1.3.3 Generalized polar s-hedra -- 1.3.4 Secant varieties and sums of powers -- 1.3.5 The Waring problems -- 1.4 Dual homogeneous forms -- 1.4.1 Catalecticant matrices -- 1.4.2 Dual homogeneous forms -- 1.4.3 The Waring rank of a homogeneous form -- 1.4.4 Mukai's skew-symmetric form -- 1.4.5 Harmonic polynomials -- 1.5 First examples -- 1.5.1 Binary forms -- 1.5.2 Quadrics -- Exercises -- Historical notes -- 2 Conics and quadric surfaces -- 2.1 Self-polar triangles -- 2.1.1 Veronese quartic surfaces -- 2.1.2 Polar lines -- 2.1.3 The variety of self-polar triangles -- 2.1.4 Conjugate triangles -- 2.2 Poncelet relation -- 2.2.1 Darboux's Theorem -- 2.2.2 Poncelet curves and vector bundles -- 2.2.3 Complex circles -- 2.3 Quadric surfaces -- 2.3.1 Polar properties of quadrics -- 2.3.2 Invariants of a pair of quadrics -- 2.3.3 Invariants of a pair of conics -- 2.3.4 The Salmon conic -- Exercises -- Historical notes -- 3 Plane cubics -- 3.1 Equations -- 3.1.1 Elliptic curves -- 3.1.2 The Hesse equation -- 3.1.3 The Hesse pencil -- 3.1.4 The Hesse group -- 3.2 Polars of a plane cubic -- 3.2.1 The Hessian of a cubic hypersurface -- 3.2.2 The Hessian of a plane cubic -- 3.2.3 The dual curve -- 3.2.4 Polar s-gons -- 3.3 Projective generation of cubic curves -- 3.3.1 Projective generation -- 3.3.2 Projective generation of a plane cubic -- 3.4 Invariant theory of plane cubics.PPN: PPN: 809893096Package identifier: Produktsigel: ZDB-26-MYL | ZDB-30-PAD | ZDB-30-PQE | BSZ-30-PQE-K1DLR

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