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Titlebook: Algebraic Geometry; An Introduction Daniel Perrin Textbook 2008 Springer-Verlag London 2008 Algebra.Arithmetic.Riemann-Roch theorem.algebra

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Dimension,(curves) and 2 (surfaces)… We will give a very natural topological definition of dimension, which is not always easy to work with, followed by other definitions which are easier to work with but which depend on results from algebra.
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Rational maps, geometric genus and rational curves,lculating primitives). We then say the curve is rational. The aim of this chapter is to give a method for calculating whether or not a curve is rational. We will prove that this is equivalent to the (geometric) genus of the curve being zero and we will give methods for calculating this geometric genus.
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P. C. Humphreys,E. L. Nappelbaumn intersections always contain a certain number of special cases due to parallel lines or asymptotes. For example, in the plane two distinct lines meet at a unique point except when they are parallel. In projective space, there are no such exceptions.
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https://doi.org/10.1007/978-3-319-42076-9lculating primitives). We then say the curve is rational. The aim of this chapter is to give a method for calculating whether or not a curve is rational. We will prove that this is equivalent to the (geometric) genus of the curve being zero and we will give methods for calculating this geometric gen
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