Birational Varieties Have the Same Dimension Algebraic Geometry Ideal Operations and Variety Operations Algebraic Geometry Affine Pieces of Projective Varieties Are Affine Varieties Algebraic Geometry Weak Nullstellensatz Algebraic Geometry Products of Projective Varieties are Projective Algebraic Geometry Proper Subvarieties of a Curve Are Finite Algebraic Geometry Plücker Embedding Algebraic Geometry Five Points Determine a Conic Algebraic Geometry