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Lectures on Geometry

  • Textbook
  • © 2024

Overview

Authors:
  1. Lucian Bădescu

    1. Department of Mathematics, University of Genoa, Genoa, Italy

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    You can also search for this author in PubMed   Google Scholar

  2. Ettore Carletti

    1. Department of Mathematics, University of Genoa (retired since 2019), Genoa, Italy

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • A comparative presentation of affine, euclidean and projective geometries
  • An elementary but complete proof of the strong Bézout’s theorem for curves of P2 (K)
  • A detailed exposition of Cayley-Klein plane geometries

Part of the book series: UNITEXT (UNITEXT, volume 158)

Part of the book sub series: La Matematica per il 3+2 (UNITEXTMAT)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xiii
    Download chapter PDF

  2. Linear Algebra

    • Lucian Bădescu, Ettore Carletti
    Pages 1-85

  3. Bilinear and Quadratic Forms

    • Lucian Bădescu, Ettore Carletti
    Pages 87-113

  4. Affine Spaces

    • Lucian Bădescu, Ettore Carletti
    Pages 115-160

  5. Euclidean Spaces

    • Lucian Bădescu, Ettore Carletti
    Pages 161-186

  6. Affine Hyperquadrics

    • Lucian Bădescu, Ettore Carletti
    Pages 187-237

  7. Projective Spaces

    • Lucian Bădescu, Ettore Carletti
    Pages 239-267

  8. Desargues’ Axiom

    • Lucian Bădescu, Ettore Carletti
    Pages 269-274

  9. General Linear Projective Automorphisms

    • Lucian Bădescu, Ettore Carletti
    Pages 275-293

  10. Affine Geometry and Projective Geometry

    • Lucian Bădescu, Ettore Carletti
    Pages 295-321

  11. Projective Hyperquadrics

    • Lucian Bădescu, Ettore Carletti
    Pages 323-383

  12. Bézout’s Theorem for Curves of \(\mathbb P^2(K)\)

    • Lucian Bădescu, Ettore Carletti
    Pages 385-419

  13. Absolute Plane Geometry

    • Lucian Bădescu, Ettore Carletti
    Pages 421-450

  14. Cayley--Klein Geometries

    • Lucian Bădescu, Ettore Carletti
    Pages 451-483

  15. Back Matter

    Pages 485-490
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Keywords

About this book

This is an introductory textbook on geometry (affine, Euclidean and projective) suitable for any undergraduate or first-year graduate course in mathematics and physics. In particular, several parts of the first ten chapters can be used in a course of linear algebra, affine and Euclidean geometry by students of some branches of engineering and computer science. Chapter 11 may be useful as an elementary introduction to algebraic geometry for advanced undergraduate and graduate students of mathematics. Chapters 12 and 13 may be a part of a course on non-Euclidean geometry for mathematics students. Chapter 13 may be of some interest for students of theoretical physics (Galilean and Einstein’s general relativity). It provides full proofs and includes many examples and exercises. The covered topics include vector spaces and quadratic forms, affine and projective spaces over an arbitrary field; Euclidean spaces; some synthetic affine, Euclidean and projective geometry; affine and projective hyperquadrics with coefficients in an arbitrary field of characteristic different from 2; Bézout’s theorem for curves of P^2 (K), where K is a fixed algebraically closed field of arbitrary characteristic; and Cayley-Klein geometries.

Authors and Affiliations

  • Department of Mathematics, University of Genoa, Genoa, Italy

    Lucian Bădescu

  • Department of Mathematics, University of Genoa (retired since 2019), Genoa, Italy

    Ettore Carletti

About the authors

Lucian Silvestru Bădescu (deceased): Graduation from University of Bucharest, Department of Mathematics, (1967), Ph. D in Mathematics, University of Bucharest (1971) with the thesis “ Rational contractions of algebraic varieties”.  Permanent position: Full professor at University of Bucharest, Department of Mathematics, until 2002, full profesor at Università degli Studi di Genova, Dipartimento di Matematica, until 2014. Field of interest: Algebric Geometry (singularities, hyperplan section and classification of projective varieties, deformation theory of singularities, arithmetic rang of projective submanifolds, algebraic surfaces, projective and formal geometry).

Ettore Carletti obtained a degree in Mathematics from the University of Genoa in 1976; he earned his Diploma di Perfezionamento in 1983. He has been a researcher in Algebra and Geometry at the University of Genoa from 1985 until 2018 when he retired. His main research focus has been zeta functions in number theory and geometry.





Bibliographic Information

  • Book Title: Lectures on Geometry

  • Authors: Lucian Bădescu, Ettore Carletti

  • Series Title: UNITEXT

  • DOI: https://doi.org/10.1007/978-3-031-51414-2

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024

  • Softcover ISBN: 978-3-031-51413-5Published: 20 April 2024

  • eBook ISBN: 978-3-031-51414-2Published: 19 April 2024

  • Series ISSN: 2038-5714

  • Series E-ISSN: 2532-3318

  • Edition Number: 1

  • Number of Pages: XIII, 490

  • Number of Illustrations: 27 b/w illustrations, 23 illustrations in colour

  • Topics: Geometry

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