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examples of varieties

• \(V(xy-t)\), a family of hyperbolas degenerating to a pair of lines.
• \(V(x^2-ty)\), a family of parabolas degenerating to a single line with multiplicity 2.
• The twisted cubic:
• Rational normal curves:
• Conifolds \(V(xy-zw) \subset {\mathbf{C}}^4\).
  • Toric with torus \(V \cap({\mathbf{C}}^*)^4 = \left\{{(x,y,z,xyz^{-1})}\right\}\).
• Generalized conifolds \(V(xy - z^{n_1} w^{n_2})\).