منابع مشابه
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First, recall how Bezout’s Theorem can be made more precise by specifying the meaning of the word “generically” used above, using elementary scheme-theoretic language ([H, II]). Fix an algebraically closed field k. There is little loss in assuming k = C (until Section 3). Since we work over an algebraically closed field, we often identify reduced algebraic sets with their k-valued points. In th...
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Let K[x, y] be the polynomial algebra in two variables over a field K of characteristic 0. In this paper, we contribute toward a classification of two-variable polynomials by classifying (up to an automorphism of K[x, y]) polynomials of the form axn + bym+ ∑ im+jn≤mn cijx iyj, a, b, cij ∈ K (i.e., polynomials whose Newton polygon is either a triangle or a line segment). Our classification has s...
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A curve that can be parametrized by polynomials is called a polynomial curve. It is well-known that a polynomial curve has only one place at infinity. Sathaye indicated the Abhyankar’s question for curves with one place at infinity. Let C be a curve with one place at infinity. Is there a polynomial curve associated with the semigroup generated by pole orders of C at infinity? We found a counter...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1955
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1955-0068860-7