Mathematics – Algebraic Geometry
Scientific paper
2008-10-09
Le Matematiche (Catania) Vol. LXII (2007) - Fasc. I, pp. 95-104
Mathematics
Algebraic Geometry
9 pages
Scientific paper
In 1980, Faltings proved, by deep local algebra methods, a local result regarding formal functions which has the following global geometric fact as a consequence. Theorem: Let k be an algebraically closed field (of any characteristic). Let Y be a closed subvariety of a projective irreducible variety X defined over k. Assume that X \subseteq P^n, dim(X)=d>2 and Y is the intersection of X with r hyperplanes of P^n, with r \le d-1. Then, every formal rational function on X along Y can be (uniquely) extended to a rational function on X. Due to its importance, the aim of this paper is to provide two elementary global geometric proofs of this theorem.
Bonacini Paola
Nesci Michele
Padrone Alessio Del
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