Residual indices of holomorphic maps relative to singular curves of fixed points on surfaces

Autor:	Filippo Bracci, Francesca Tovena
Rok vydání:	2002
Předmět:	Pointwise Combinatorics General Mathematics Mathematical analysis Holomorphic function Point (geometry) Complex manifold Fixed point Residual Identity theorem Degeneracy (mathematics) Mathematics
Zdroj:	Mathematische Zeitschrift. 242:481-490
ISSN:	1432-1823 0025-5874
DOI:	10.1007/s002090100352
Popis:	Let M be a two-dimensional complex manifold and let \(f:M\to M\) be a holomorphic map that fixes pointwise a (possibly) singular, compact, reduced and globally irreducible curve \(C\subset M\). We give a notion of degeneracy of f at a point of C. It turns out that f is non-degenerate at one point if and only if it is non-degenerate at every point of C. When f is non-degenerate on C, we define a residual index for f at each point of C. Then we prove that the sum of the indices is equal to the self-intersection number of C.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::23ae55410a2994c7c79f45b6dbb44b61 https://doi.org/10.1007/s002090100352 Zobrazit plný text záznamu Full text from SpringerLink