The study of geometric objects defined by polynomial equations, as well as their generalizations: algebraic curves, such as elliptic curves, and more generally algebraic varieties, schemes, etc. Problems under this tag typically involve techniques of abstract algebra or complex-analytic methods. ...

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Plücker relations for $Gr_2(\mathbb{C}^5)$

I know that for the complex Grassmannian $Gr_2(\mathbb{C}^4)$, with the index sets $I= \{1,2\}, J = \{3,4\}$, the Pl├╝cker relation is given by $$ P_{12}P_{34} - P_{32}P_{14} - P_{13}P_{24} =0 \text{,} ...
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Topology of Isolated Singularities

In Singular Points of Complex Hypersurfaces, Milnor shows that if $f: \mathbb{C}^{n+1} \rightarrow \mathbb{C}$, holomorphic, has an isolated singularity at the origin, then $f^{-1}(\epsilon) \cap ...