Divisors and Differential Forms

Igor R. Shafarevich
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Igor R. Shafarevich: Steklov Mathematical Institute

Chapter Chapter III in Basic Algebraic Geometry 1, 1994, pp 151-222 from Springer

Abstract: Abstract A polynomial in one variable is uniquely determined up to a constant factor by specifying its roots and their multiplicities; that is by specifying a set of points x 1,…,x r ∈ A1 with multiplicities k 1 …,k r. A rational function ϕ(x) = f(x)/g(x) with f,g ∈ k[A1] is determined by the zeros of f and g, that is, by the points at which it is 0 or is irregular. To distinguish the roots of g from those of f, we take their multiplicities with a minus sign. Thus the function ϕ is given by points x 1, …,x r with arbitrary integer multiplicities K 1,… , K r.

Keywords: Algebraic Group; Differential Form; Abelian Variety; Prime Divisor; Hyperelliptic Curve (search for similar items in EconPapers)
Date: 1994
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DOI: 10.1007/978-3-642-57908-0_3

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