Local Freeness of Differentials Algebraic Geometry $\mathbb{P}^1_k \times \mathbb{P}^1_k \not\cong \mathbb{P}^2_k$ Algebraic Geometry Riemann–Hurwitz Formula Algebraic Geometry Curves of Degree at Most 2 Meet in at Most 4 Points Algebraic Geometry Normal Form for Quadrics Algebraic Geometry Element Outside $\mathfrak{m}_p^2$ Generates $\mathfrak{m}_p$ Algebraic Geometry Dimension as Transcendence Degree Algebraic Geometry Unique Effective Representative When $\ell(D) = 1$ Algebraic Geometry