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Algebraic Varieties

  • Mario Baldassarri
Conference proceedings

Part of the Ergebnisse der Mathematik und Ihrer Grenzgebiete book series (MATHE2, volume 12)

Table of contents

  1. Front Matter
    Pages II-XI
  2. Mario Baldassarri
    Pages 26-36
  3. Mario Baldassarri
    Pages 47-64
  4. Mario Baldassarri
    Pages 64-83
  5. Mario Baldassarri
    Pages 102-125
  6. Mario Baldassarri
    Pages 162-178

About these proceedings

Introduction

Algebraic geometry has always been an ec1ectic science, with its roots in algebra, function-theory and topology. Apart from early resear­ ches, now about a century old, this beautiful branch of mathematics has for many years been investigated chiefly by the Italian school which, by its pioneer work, based on algebro-geometric methods, has succeeded in building up an imposing body of knowledge. Quite apart from its intrinsic interest, this possesses high heuristic value since it represents an essential step towards the modern achievements. A certain lack of rigour in the c1assical methods, especially with regard to the foundations, is largely justified by the creative impulse revealed in the first stages of our subject; the same phenomenon can be observed, to a greater or less extent, in the historical development of any other science, mathematical or non-mathematical. In any case, within the c1assical domain itself, the foundations were later explored and consolidated, principally by SEVERI, on lines which have frequently inspired further investigations in the abstract field. About twenty-five years ago B. L. VAN DER WAERDEN and, later, O. ZARISKI and A. WEIL, together with their schools, established the methods of modern abstract algebraic geometry which, rejecting the c1assical restriction to the complex groundfield, gave up geometrical intuition and undertook arithmetisation under the growing influence of abstract algebra.

Keywords

Abstract algebra Mathematica algebra algebraic geometry cohomology development field function geometry knowledge manifold mathematics topology transformation

Authors and affiliations

  • Mario Baldassarri
    • 1
  1. 1.PadovaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-52761-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 1956
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-52763-0
  • Online ISBN 978-3-642-52761-6
  • Series Print ISSN 0071-1136
  • Buy this book on publisher's site
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