Intersection theory

Preface......Page page000004.djvu
Contents......Page page000008.djvu
Introduction......Page page000014.djvu
1.1. Notation and Conventions......Page page000019.djvu
1.2. Orders of Zeros and Poles......Page page000021.djvu
1.3. Cycles and Rational Equivalence......Page page000023.djvu
1.4. Push-forward of Cycles......Page page000024.djvu
1.6. Alternate Definition of Rational Equivalence......Page page000028.djvu
1.7. Flat Pull-back of Cycles......Page page000031.djvu
1.8. An Exact Sequence......Page page000034.djvu
1.9. Affine Bundles......Page page000035.djvu
1.10. Exterior Products......Page page000037.djvu
Notes and References......Page page000038.djvu
Summary......Page page000041.djvu
2.1. Cartier Divisors and Wei1 Divisors......Page page000042.djvu
2.2. Line Bundles and Pseudo-divisors......Page page000044.djvu
2.3. Intersecting with Divisors......Page page000046.djvu
2.4. Commutativity ofIntersection Classes......Page page000048.djvu
2.5. Chern Class of a Line Bundle......Page page000054.djvu
2.6. Gysin Map for Divisors......Page page000056.djvu
Notes and References......Page page000058.djvu
3.1. Segre Classes of Vector Bundles......Page page000060.djvu
3.2. Chern Classes......Page page000063.djvu
3.3. Rational Equivalence on Bundles......Page page000077.djvu
Notes and References......Page page000081.djvu
4.1. Segre Class of a Cone......Page page000083.djvu
4.2. Segre Class of a Subscheme......Page page000086.djvu
4.3. Multiplicity Along a Subvariety......Page page000092.djvu
4.4. Linear Systems......Page page000095.djvu
Notes and References......Page page000098.djvu
5.1. The Deformation......Page page000099.djvu
5.2. Specialization to the Normal Cone......Page page000102.djvu
Notes and References......Page page000103.djvu
Summary......Page page000105.djvu
6.1. The Basic Construction......Page page000106.djvu
6.2. Refined Gysin Homomorphisms......Page page000110.djvu
6.3. Excess Intersection Formula......Page page000115.djvu
6.4. Commutativity......Page page000119.djvu
6.5. Functoriality......Page page000121.djvu
6.6. Local Complete Intersection Morphisms......Page page000125.djvu
6.7. Monoidal Transforms......Page page000127.djvu
Notes and References......Page page000130.djvu
7.1. Proper Intersections......Page page000132.djvu
7.2. Criterion for Multiplicity One......Page page000139.djvu
Notes and References......Page page000140.djvu
8.1. Refined Intersections......Page page000143.djvu
8.2. Intersection Multiplicities......Page page000150.djvu
8.3. Intersection Ring......Page page000153.djvu
8.4. Bezout\'s Theorem (Classical Version)......Page page000157.djvu
Notes and References......Page page000164.djvu
9.1. Equivalence of a Connected Component......Page page000166.djvu
9.2. Residual Intersection Theorem......Page page000173.djvu
9.3. Double Point Formula......Page page000178.djvu
Notes and References......Page page000184.djvu
Summary......Page page000188.djvu
10.1. Families of Cycle Classes......Page page000189.djvu
10.2. Conservation of Number......Page page000193.djvu
10.3. Algebraic Equivalence......Page page000198.djvu
10.4. An Enumerative Problem......Page page000200.djvu
Notes and References......Page page000206.djvu
Summary......Page page000208.djvu
11.1. Limits of Intersection Classes......Page page000209.djvu
11.2. Infinitesimal Intersection Classes......Page page000211.djvu
11.3. Limits and Distinguished Varieties......Page page000213.djvu
11.4. Moving Lemmas......Page page000218.djvu
Notes and References......Page page000222.djvu
Summary......Page page000223.djvu
12.1. Positive Vector Bundles......Page page000224.djvu
12.2. Positive Intersections......Page page000231.djvu
12.3. Refined Bezout Theorem......Page page000236.djvu
12.4. Intersection Multiplicities......Page page000240.djvu
Notes and References......Page page000247.djvu
Summary......Page page000248.djvu
Notes and References......Page page000254.djvu
Summary......Page page000255.djvu
14.1. Localized Top Chern Class......Page page000257.djvu
14.2. Gysin Formulas......Page page000260.djvu
14.3. Determinanta1 Formula......Page page000262.djvu
14.4. Thorn-Porteous Formula......Page page000267.djvu
14.5. Schur Polynomials......Page page000276.djvu
14.6. Grassmann Bundles......Page page000279.djvu
14.7. Schubert Calculus......Page page000284.djvu
Notes and References......Page page000291.djvu
15.1. Preliminaries......Page page000293.djvu
15.2. Grothendieck-Riemann-Roch Theorem......Page page000299.djvu
15.3. Riemann-Roch Without Denominators......Page page000309.djvu
15.4. Blowing up Chern Classes......Page page000311.djvu
Notes and References......Page page000315.djvu
16.1. Algebra of Correspondences......Page page000318.djvu
16.2. Irregular Fixed Points......Page page000328.djvu
Notes and References......Page page000331.djvu
Summary......Page page000332.djvu
17.1. Bivariant Rational Equivalence Classes......Page page000333.djvu
17.2. Operations and Properties......Page page000335.djvu
17.3. Homology and Cohomology......Page page000337.djvu
17.4. Orientations......Page page000339.djvu
17.5. Monoida1 Transforms......Page page000345.djvu
17.6. Residual Intersection Theorem......Page page000346.djvu
Notes and References......Page page000350.djvu
Summary......Page page000352.djvu
18.1. Graph Construction......Page page000353.djvu
18.2. Riemann-Roch for Quasi-projective Schemes......Page page000361.djvu
18.3. Riemann-Roch for Algebraic Schemes......Page page000366.djvu
Notes and References......Page page000381.djvu
Summary......Page page000383.djvu
19.1. Cycle Map......Page page000384.djvu
19.2. Algebraic and Topological Intersections......Page page000391.djvu
19.3. Equivalence on Non-singular Varieties......Page page000398.djvu
Notes and References......Page page000404.djvu
20.1. Schemes Over a Regular Base Scheme......Page page000406.djvu
20.2. Schemes Over a Dedekind Domain......Page page000410.djvu
20.3. Specialization......Page page000411.djvu
20.4. Tor and Intersection Products......Page page000414.djvu
20.5. Higher K-theory......Page page000416.djvu
Notes and References......Page page000417.djvu
A.1. Length......Page page000419.djvu
A.2. Herbrand Quotients......Page page000420.djvu
A.3. Order Functions......Page page000424.djvu
A.4. Flatness......Page page000426.djvu
A.5. Koszul Complexes......Page page000427.djvu
A.6. Regular Sequences......Page page000429.djvu
A.7. Depth......Page page000431.djvu
A.9. Determinantal Identities......Page page000432.djvu
Notes and References......Page page000438.djvu
B.1. Algebraic Schemes......Page page000439.djvu
B.2. Morphisms......Page page000440.djvu
B.3. Vector Bundles......Page page000443.djvu
B.4. Cartier Divisors......Page page000444.djvu
B.5. Projective Cones and Bundles......Page page000445.djvu
B.6. Normal Cones and Blowing Up......Page page000448.djvu
B.7. Regular Imbeddings and l.c.i. Morphisms......Page page000450.djvu
B.8. Bundles on Imbeddable Schemes......Page page000452.djvu
B.9. General Position......Page page000453.djvu
Bibliography......Page page000455.djvu
Notation......Page page000475.djvu
Index......Page page000477.djvu