Varieties and projective geometry
Classical algebraic geometry of affine and projective varieties: hypersurfaces and their singularities, tangent spaces, plane configurations, intersection multiplicities, linear systems and birational maps.
- Birational maps and the Cremona group
- Bézout's theorem
- Cubic surfaces
- Equimultiplicity of μ-constant families
- Fields of definition of algebraic sets
- Line arrangements in the projective plane
- Multiplicity of a hypersurface at a point
- Regular functions on algebraic sets
- Seshadri constants of points in the plane
- Tangent spaces of algebraic sets
- Topological reconstruction of varieties
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