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algebraic-geometry
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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.