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Cohomology theory and algebraic correspondences

About this Title

Ernst Snapper

Publication: Memoirs of the American Mathematical Society
Publication Year: 1959; Number 33
ISBNs: 978-0-8218-1233-4 (print); 978-0-8218-9976-2 (online)
DOI: https://doi.org/10.1090/memo/0033
MathSciNet review: 0104673

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Table of Contents

Chapters

  • Introduction
  • Topological preparations
  • Part I. The cohomology theorem of the graph
  • 1. The proper generalization of Lemma 14.1 of [3]
  • 2. Applications of Lemma 1.1
  • Part II. Sheaves, associated with doubly graded modules
  • 3. The doubly graded coordinate ring of an algebraic correspondence
  • 4. Sheaves of fractional ideals
  • 5. The sheaf of a doubly graded $v$-module
  • 6. The sheaf $A(v^*(m, n))$
  • 7. Integrally closed Noetherian rings
  • 8. Divisors
  • Part III. Cohomology groups of doubly graded modules
  • 9. The double complex of a doubly graded $v$-module
  • 10. Polynomials
  • 11. General properties of $H^t(\mathfrak {M})$
  • 12. General properties of $H^t(X_3, F)$
  • 13. The divisor $D(m, n)$
  • Part IV. Linear systems
  • 14. Completeness of $g(m, n)$
  • 15. The Hilbert characteristic function of $T$
  • 16. The polynomial $\chi _1(m)$
  • 17. Irreducible linear systems without base points
  • Part V. The geometric genus under birational transformations
  • 18. Affine subvarieties, associated with $T$
  • 19. Coverings, associated with $T$
  • 20. Cohomology groups under birational transformations