By Gerd Fischer
The examine of the zeroes of polynomials, which for one variable is largely algebraic, turns into a geometrical concept for numerous variables. during this e-book, Fischer appears to be like on the vintage access element to the topic: airplane algebraic curves. right here one quick sees the combo of algebra and geometry, in addition to research and topology, that's standard of complicated algebraic geometry, yet with out the necessity for complex suggestions from commutative algebra or the summary equipment of sheaves and schemes. within the first half this booklet, Fischer introduces a few easy geometrical elements, comparable to tangents, singularities, inflection issues, etc. the most technical software is the concept that of intersection multiplicity and BÃ©zout's theorem. This half culminates within the attractive PlÃ¼cker formulation, which relate some of the invariants brought past. the second one a part of the e-book is largely an in depth define of recent equipment of neighborhood analytic geometry within the context of complicated curves. this gives the greater instruments wanted for an outstanding figuring out of duality and a good technique of computing intersection multiplicities brought previous. hence, we meet jewelry of strength sequence, germs of curves, and formal parametrizations. eventually, throughout the patching of the neighborhood info, a Riemann floor is linked to an algebraic curve, therefore linking the algebra and the research.
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