In this paper we study the fibers of a rational map from an algebraic point of view. We begin by describing four ideals related to such a fiber.rnLet S = k [x_0,..., x_n] be a polynomial ring over an infinite field k with homogeneous maximal ideal m, let I is contained in S be an ideal generated by an (r + 1)-dimensional vector space W of forms of the same degree, and let φ be the associated rational map P~n → P~r = P(W). We will use this notation throughout. Since we are interested in the rational map, we may remove common divisors of W and thus assume that I has codimension ≥ 2.
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机译：在本文中，我们从代数的角度研究有理图的纤维。我们从描述与这种纤维相关的四个理想开始。rnL S = k [x_0，...，x_n]是无限场k上具有齐次最大理想m的多项式环，令I包含在S中是生成的理想通过（r + 1）维具有相同度数形式的向量空间W，令φ为相关的有理图P〜n→P〜r = P（W）。我们将在整个过程中使用此表示法。由于我们对有理图感兴趣，因此我们可以删除W的公因数，并假设I的余数≥2。
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