Vanishing theorems, linear and quadratic normality

DOI10.1007/BF01389243zbMath0618.14023MaRDI QIDQ1089058

Thomas Peternell, Michael Schneider, Joseph Le Potier

Publication date: 1987

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143436

zbMATH Keywords

complete intersectionHartshorne conjecturesmall codimension

Mathematics Subject Classification ID

Complete intersections (14M10) Low codimension problems in algebraic geometry (14M07) Vanishing theorems (32L20)

Related Items (14)

Barth type vanishing theorem ⋮ Corrigenda to ``Barth type vanishing theorems ⋮ Vanishing theorems for tensor powers of an ample vector bundle ⋮ Direct images of sheaves of differentials and the Atiyah class ⋮ Vector bundles generated by sections and ample ⋮ Topological methods in moduli theory ⋮ Generalization of Peternell, le Potier and Schneider vanishing theorem ⋮ On the 3 and 4-normality of codimension two subvarieties of \({\mathbb{P}}^ n\) ⋮ Vanishing theorems for vector bundles generated by sections ⋮ (k, s)-POSITIVITY AND VANISHING THEOREMS FOR COMPACT KÄHLER MANIFOLDS ⋮ Positivity and vanishing theorems for ample vector bundles ⋮ Sur la cohomologie des fibrés associés au fibré quotient universel sur la grassmannienne ⋮ On the normal bundle of submanifolds of $\mathbb P^n$ ⋮ Unnamed Item

Cites Work

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• Some remarks on vanishing theorems for holomorphic vector bundles
• Direct images of sheaves of differentials and the Atiyah class
• Annulation de la cohomologie à valeurs dans un fibre vectoriel holomorphe positif de rang quelconque
• Submanifolds of Abelian varieties
• Ample subvarieties of algebraic varieties. Notes written in collaboration with C. Musili
• The positivity of the Chern classes of an ample vector bundle
• A computer aided approach to codimension 2 subvarities of Pn, n6.
• Verschwindungssätze und Untermannigfaltigkeiten kleiner Kodimension des komplex-projektiven Raumes.
• Varieties of small codimension in projective space
• Transplanting Cohomology Classes in Complex-Projective Space

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