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Cohomology Theory and Algebraic Correspondences
eBook ISBN:  9780821899762 
Product Code:  MEMO/1/33.E 
List Price:  $23.00 
MAA Member Price:  $20.70 
AMS Member Price:  $18.40 
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Cohomology Theory and Algebraic Correspondences
eBook ISBN:  9780821899762 
Product Code:  MEMO/1/33.E 
List Price:  $23.00 
MAA Member Price:  $20.70 
AMS Member Price:  $18.40 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 1; 1959; 96 ppMSC: Primary 14

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


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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
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