Space · region

Algebraic geometry

The geometry of solution sets of polynomial equations. Its biggest open questions ask which shapes can be cut out by polynomials and when a polynomial map can be undone.

Mathematics Subject Classification: 14.

Problems

Jacobian conjecture, n ≥ 3 (refuted)
Jacobian conjecture in the plane (open)
Hodge conjecture (open)
Weil conjectures (solved)
Resolution of singularities in characteristic p (open)

Part of Mathematics.

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