Abstract
In this paper we establish an arithmetic Riemann-Roch-Grothendieck Theorem for immersions. Our final formula involves the Bott-Chern currents attached to certain holomorphic complexes of Hermitian vector bundles, which were previously introduced by the authors. The functorial properties of such currents are studied. Explicit formulas are given for Koszul complexes.
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Bismut, JM., Gillet, H., Soulé, C. (2007). Complex Immersions and Arakelov Geometry. In: Cartier, P., Illusie, L., Katz, N.M., Laumon, G., Manin, Y.I., Ribet, K.A. (eds) The Grothendieck Festschrift. Progress in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4574-8_8
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DOI: https://doi.org/10.1007/978-0-8176-4574-8_8
Publisher Name: Birkhäuser, Boston, MA
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