Algebraic Varieties

1. Front Matter

   Pages II-XI

   PDF

2. Linear Systems

   • Mario Baldassarri

   Pages 26-36

3. The Arithmetic Genus

   • Mario Baldassarri

   Pages 47-64

4. Algebraic and Rational Equivalence

   • Mario Baldassarri

   Pages 64-83

5. The Abelian Varieties from the Algebraic Viewpoint; and Related Questions

   • Mario Baldassarri

   Pages 83-102

6. Theory and Applications of the Canonical Systems

   • Mario Baldassarri

   Pages 102-125

7. The Algebraic Varieties as Complex-analytic Manifolds

   • Mario Baldassarri

   Pages 125-140

8. The Superficial Irregularity and Continuous Systems

   • Mario Baldassarri

   Pages 162-178

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.

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

• Padova, Italy

  Mario Baldassarri

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