A Grothendieck-Riemann-Roch formula for maps of complex manifolds

DOI10.1007/BF01456132zbMath0539.14005OpenAlexW1985412052MaRDI QIDQ793795

Nigel R. O'Brian, Yue Lin L. Tong, Domingo Toledo

Publication date: 1985

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

Full work available at URL: https://eudml.org/doc/163984

zbMATH Keywords

Serre-Grothendieck dualityGrothendieck-Riemann-Roch formulaHodge cohomologymap of complex manifoldstwisting cochains

Mathematics Subject Classification ID

Riemann-Roch theorems (14C40) Sheaves and cohomology of sections of holomorphic vector bundles, general results (32L10) Complex manifolds (32Q99) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30)

Related Items (14)

Algebraic index theorem ⋮ Kähler geometry of Douady spaces ⋮ Descent of dg cohesive modules for open covers on complex manifolds ⋮ The Weil–Petersson current on Douady spaces ⋮ Simplicial Chern-Weil theory for coherent analytic sheaves. II ⋮ Instantons and curves on class VII surfaces ⋮ Twisted complexes on a ringed space as a dg-enhancement of the derived category of perfect complexes ⋮ HIRZEBRUCH CLASSES AND MOTIVIC CHERN CLASSES FOR SINGULAR SPACES ⋮ Automorphisms and autoequivalences of generic analytic \(K3\) surfaces ⋮ Chern classes in Deligne cohomology for coherent analytic sheaves ⋮ Twisted complexes and simplicial homotopies ⋮ Todd class via homotopy perturbation theory ⋮ Unnamed Item ⋮ Analytic cycles, Bott-Chern forms, and singular sets for the Yang-Mills flow on Kähler manifolds

Cites Work

• Résidus et dualité
• A parametrix for \(\overline\partial\) and Riemann-Roch in Cech theory
• Duality and intersection theory in complex manifolds. I
• Dualité relative en géométrie analytique complexe
• On the groups \(H(\Pi,n)\). I
• On the groups \(H(\Pi,n)\). II
• Le théorème de Riemann-Roch
• The Trace Map and Characteristic Classes for Coherent Sheaves
• Hirzebruch-Riemann-Roch for Coherent Sheaves
• Grothendieck-Riemann-Roch for complex manifolds

This page was built for publication: A Grothendieck-Riemann-Roch formula for maps of complex manifolds