Download E-books Plane Algebraic Curves (Student Mathematical Library, V. 15) PDF

By Gerd Fischer

The examine of the zeroes of polynomials, which for one variable is largely algebraic, turns into a geometrical idea for a number of variables. during this e-book, Fischer seems to be on the vintage access element to the topic: aircraft algebraic curves. right here one speedy sees the combination of algebra and geometry, in addition to research and topology, that's regular of complicated algebraic geometry, yet with no the necessity for complex innovations from commutative algebra or the summary equipment of sheaves and schemes. within the first 1/2 this publication, Fischer introduces a few simple geometrical features, akin to tangents, singularities, inflection issues, etc. the most technical instrument is the concept that of intersection multiplicity and Bézout's theorem. This half culminates within the attractive Plücker formulation, which relate a few of the invariants brought past. the second one a part of the ebook is largely a close define of contemporary tools of neighborhood analytic geometry within the context of advanced curves. this offers the more desirable instruments wanted for an outstanding knowing of duality and an effective technique of computing intersection multiplicities brought previous. hence, we meet earrings of strength sequence, germs of curves, and formal parametrizations. eventually, during the patching of the neighborhood details, a Riemann floor is linked to an algebraic curve, therefore linking the algebra and the research.

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