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# Tag Archives: Zariski cotangent space

## Lecture 15: Monday, September 23, 2013

Today we discuss how some familiar objects — namely the circle, the sphere, the torus, and even elliptic curves — are each examples of non-singular algebraic curves which are also compact, connected Riemann surfaces. Advertisements

## Lecture 14: Friday, September 20, 2013

Eventually, we wish to show that every compact, connected Riemann surface is a nonsingular algebraic curve. Today, we discuss what is means to be a “nonsingular algebraic curve” using Dedekind Domains.

Posted in MA 59800
Tagged Algebraic Curve, Algebraic Variety, Coordinate ring, Dedekind domain, Discrete Valuation, Discrete Valuation Ring, Integral domain, Jacobian matrix, Localization, Maximal ideal, Oscar Zariski, Polynomial ring, Prime ideal, Principal Ideal, Radical of an Ideal, Tangent space, Zariski cotangent space
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