Duality and intersection theory in complex manifolds. I

DOI10.1007/BF01351557zbMath0391.32008MaRDI QIDQ1251321

Domingo Toledo, Yue Lin L. Tong

Publication date: 1978

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/182776

zbMATH Keywords

DualityExtIntersection TheoryCoherent SheafComplex ManifoldsConnection CocycleGysin MapsHirzebruch-Riemann-Roch TheoremHolomorphic Lefschetz FormulaTwisted Cech Cochains and Complexes

Mathematics Subject Classification ID

Riemann-Roch theorems (14C40) Sheaves and cohomology of sections of holomorphic vector bundles, general results (32L10) Duality theorems for analytic spaces (32C37)

Related Items (15)

Intersections of higher-weight cycles over quaternionic modular surfaces and modular forms of Nebentypus ⋮ Determinant bundles and Virasoro algebras ⋮ The Hodge Chern character of holomorphic connections as a map of simplicial presheaves ⋮ Descent of dg cohesive modules for open covers on complex manifolds ⋮ Unnamed Item ⋮ The higher Riemann-Hilbert correspondence ⋮ HF=HM. V: Seiberg-Witten Floer homology and handle additions ⋮ The Ext algebra of a quantized cycle ⋮ Twisted complexes on a ringed space as a dg-enhancement of the derived category of perfect complexes ⋮ Unnamed Item ⋮ Twisted complexes and simplicial homotopies ⋮ Todd class via homotopy perturbation theory ⋮ Unnamed Item ⋮ A Grothendieck-Riemann-Roch formula for maps of complex manifolds ⋮ Grothendieck-Riemann-Roch for complex manifolds

Cites Work

• Unnamed Item
• Un théorème de dualité
• A parametrix for \(\overline\partial\) and Riemann-Roch in Cech theory
• Local cohomology. A seminar given by A. Grothendieck, Harvard University, Fall 1961. Notes by R. Hartshorne
• Complexe dualisant et théorèmes de dualité en géométrie analytique complexe
• Residues and duality. Lecture notes of a seminar on the work of A. Grothendieck, given at Havard 1963/64. Appendix: Cohomology with supports and the construction of the \(f^!\) functor by P. Deligne
• Introduction to Grothendieck duality theory
• La théorie des classes de Chern
• The holomorphic Lefschetz formula

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