UID:
almahu_9947359870402882
Umfang:
Online-Ressource (xx, 398 p)
Ausgabe:
Online-Ausg. Palo Alto, Calif ebrary 2011 Electronic reproduction; Available via World Wide Web
ISBN:
3110143550
,
9783110143553
,
9783110871746
Serie:
De Gruyter expositions in mathematics 16
Inhalt:
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
Anmerkung:
Includes bibliographical references and index
,
10.3 Very ampleness of the adjoint bundle.
,
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.
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8.6 Surfaces with Castelnuovo curves as hyperplane sections8.7 Polarized varieties (X, L) with sectional genus g(L) = h1(OX); 8.8 Spannedness of KX + (dim X)L for ample and spanned L; 8.9 Polarized varieties (X, L) with sectional genus g(L) ≤ 1; 8.10 Classification of varieties up to degree 4; Chapter 9. The adjunction mapping; 9.1 Spannedness of adjoint bundles at singular points; 9.2 The adjunction mapping; Chapter 10. Classical adjunction theory of surfaces; 10.1 When the adjunction mapping has lower dimensional image; 10.2 Surfaces with sectional genus g(L) ≤ 3.
,
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.
Sprache:
Englisch
DOI:
10.1515/9783110871746
URL:
http://www.degruyter.com/doi/book/10.1515/9783110871746
