New answers tagged algebraic-curves
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Parameterisatio of Curve in projective space
This is not easy to visualize; this is a coordinate transformation $\mathbb{R}^3 \to \mathbb{R}^3$. In fact, this is a linear transformation. Can you find the matrix representing it? Examples of these ...
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What is a local parameter in algebraic geometry?
In the second-to-last paragraph from Matt E's answer they interpret uniformizers of a stalk of the sheaf of algebraic functions leveraging the analytic topology. The case of the sheaf of analytic ...
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What must be true for thirteen points to impose independent conditions on quartics?
Actually I think Theorem (CB5) from the Eisenbud, Green, Harris paper gives you exactly what you are asking about. At least it gives the following: Let C and D be plane quartics with no common ...
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smooth proper connected curve over a field is projective
The proof given in the link does not need algebraic closure of $k$ - the key steps in the proof are that normalization over a field is a finite morphism, finite morphisms are projective, and the curve ...
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Line bundles on singular curves
There is also the following more straightforward approach. Consider the plane model of your curve $X$. Call it $X'$. Let p be the node of X' which is the image of the node of X. Now any line l through ...
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Maximal number of multiple points for an irreducible quartic
If three of the multiple points are collinear, then the line through these three multiple points has intersection multiplicity at least 6 with the quartic, contradicting Bezout. If no three of these ...
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