An adelic construction of Chern classes

Journal Article · Wed Nov 30 00:00:00 EST 2011 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2011V202N11ABEH004202; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21612803

Budylin, Roman Ya ^[1]

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1. M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

We give a formula expressing the second Chern class c{sub 2}(E) in terms of trivializations of a rank two vector bundle E at scheme points of a surface X over a field. To do this, starting with these trivializations, we construct a cocycle in the adelic complex associated with the sheaf K{sub 2}(O{sub X}). Furthermore we prove that the Severi formula for the second Chern class is obtained as a special case of the formula constructed in this work. Bibliography: 10 titles.

• OSTI ID: 21612803
• Journal Information: Sbornik. Mathematics, Vol. 202, Issue 11; Other Information: DOI: 10.1070/SM2011v202n11ABEH004202; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
CALCULATION METHODS
COMPLEX MANIFOLDS
MATHEMATICAL LOGIC
SURFACES
VECTORS
MATHEMATICAL MANIFOLDS
TENSORS