Cubic plane curve

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Explores plane curves, focusing on singular points, multiplicities, and tangent lines.

Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.

Explores ellipse construction using the Dandelin theorem and properties of conics in space.

Explores irreducible algebraic sets and their unique decomposition into components, with a focus on prime ideals and plane subsets classification.

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Explores affine varieties, hypersurfaces, dimension in algebraic geometry, minimal prime ideals, and local properties of plane curves.

Explores Bézout's theorem and Cayley-Bacharach, discussing intersection multiplicities and linear combinations in projective geometry.