I've read the wikipedia article but I don't know what an affine plane is and the definition/example did not seem clear. What I know is that in the 1880s mathematicians like Hilbert, Kronecker, Lasky and Macauley were responsible for the development of the algebraic variety concept. This is for a history of mathematics paper that I am working on.
Could someone give me an example of an algebraic variety and explain what it is
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abstract-algebra
algebraic-geometry
math-history
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0As far as I know, Algebraic varieties are (irreducible) set of solutions of a polynomial equation. Affine spaces are very similar to a linear space but with no real attention being paid to the existence of an origin, zero element (in a vector space, one of the axioms required the zero element to be a part of the space, in an affine space, that is no matter of concern really) – 2012-03-27
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3Why isn't this sufficient: http://en.wikipedia.org/wiki/Algebraic_variety ? – 2012-03-27
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0I don't have the math background to understand that article. – 2012-03-27
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6You've told us what you don't understand, but you haven't told us what you *do* understand, so it's hard to know where to begin. – 2012-03-27
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0Maybe you mean Lasker, better known as one of the great chess players. Or maybe Lansky, who as far as I know was not interested in research mathematics, but used his mathematical talents in the service of the Mob. – 2012-03-27
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1*An Invitation to Algebraic Geometry* by Smith, Kahanpaa, Kekalainen, and Traves is a very accesible text written at the undergraduate level. Dieudonne's *History of Algebraic Geometry* will likely be useful to connect the dots historically. – 2012-03-27
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1Are you trying to write a paper about the historical development of 19th century algebra and geometry without understanding the related mathematical ideas? If so, I think you have not chosen a topic well. Getting stuck on the meaning of the affine plane does not put you in a good position to see the point of the work of Hilbert, Kronecker, et al., since it appears that you can't give an example of the objects that interested them. – 2012-03-28