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E-book
Author Sommese, Andrew J

Title The Adjunction Theory of Complex Projective Varieties
Published Berlin : De Gruyter, 1995

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Description 1 online resource (420 pages)
Series De Gruyter Expositions in Mathematics ; v. 16
De Gruyter expositions in mathematics.
Contents Preface; List of tables; Chapter 1. General background results; 1.1 Some basic definitions; 1.2 Surface singularities; 1.3 On the singularities that arise in adjunction theory; 1.4 Curves; 1.5 Nefvalue results; 1.6 Universal sections and discriminant varieties; 1.7 Bertini theorems; 1.8 Some examples; Chapter 2. Consequences of positivity; 2.1 k-ampleness and k-bigness; 2.2 Vanishing theorems; 2.3 The Lefschetz hyperplane section theorem; 2.4 The Albanese mapping in the presence of rational singularities; 2.5 The Hodge index theorem and the Kodaira lemma; 2.6 Rossi's extension theorems
2.7 Theorems of Andreotti-Grauert and GriffithsChapter 3. The basic varieties of adjunction theory; 3.1 Recognizing projective spaces and quadrics; 3.2 Pd-bundles; 3.3 Special varieties arising in adjunction theory; Chapter 4. The Hilbert scheme and extremal rays; 4.1 Flatness, the Hilbert scheme, and limited families; 4.2 Extremal rays and the cone theorem; 4.3 Varieties with nonnef canonical bundle; Chapter 5. Restrictions imposed by ample divisors; 5.1 On the behavior of k-big and ample divisors under maps; 5.2 Extending morphisms of ample divisors
5.3 Ample divisors with trivial pluricanonical systems5.4 Varieties that can be ample divisors only on cones; 5.5 Pd-bundles as ample divisors; Chapter 6. Families of unbreakable rational curves; 6.1 Examples; 6.2 Families of unbreakable rational curves; 6.3 The nonbreaking lemma; 6.4 Morphisms of varieties covered by unbreakable rational curves; 6.5 The classification of projective manifolds covered by lines; 6.6 Some spannedness results; Chapter 7. General adjunction theory; 7.1 Spectral values; 7.2 Polarized pairs (M, L) with nefvalue> dim M -- l and M singular
7.3 The first reduction of a singular variety7.4 The polarization of the first reduction; 7.5 The second reduction in the smooth case; 7.6 Properties of the first and the second reduction; 7.7 The second reduction (X, D) with KX + (n -- 3) D nef; 7.8 The three dimensional case; 7.9 Applications; Chapter 8. Background for classical adjunction theory; 8.1 Numerical implications of nonnegative Kodaira dimension; 8.2 The double point formula for surfaces; 8.3 Smooth double covers of irreducible quadric surfaces; 8.4 Surfaces with one dimensional projection from a line; 8.5 k-very ampleness
Summary An overview of developments in the past 15 years of adjunction theory, the study of the interplay between the intrinsic geometry of a projective variety and the geometry connected with some embedding of the variety into a projective space. Topics include consequences of positivity, the Hilbert schem
Notes Print version record
Subject Adjunction theory.
Embeddings (Mathematics)
Algebraic varieties.
Projective spaces.
Adjunction theory
Algebraic varieties
Embeddings (Mathematics)
Projective spaces
Form Electronic book
Author Beltrametti, Mauro C
ISBN 9783110871746
3110871742