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An Introduction to Algebraic Geometry: Polygons, Parameterizations, and Equations

Jessica Sidman
The American Mathematical Monthly
Vol. 119, No. 3 (March 2012), pp. 183-198
DOI: 10.4169/amer.math.monthly.119.03.183
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.119.03.183
Page Count: 16
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An Introduction to Algebraic Geometry: Polygons, Parameterizations, and Equations
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Abstract

Abstract We explain how four surfaces that are ubiquitous in algebraic geometry may be obtained from convex polygons whose vertices have integer coordinates, realizing these surfaces as examples of toric varieties. We highlight the combinatorial and algebraic properties revealed by this construction. Our claim of novelty is in our particular combination of the toric, classical geometric, and algebraic points of view.

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