# Algebraic geometry

- kind: region

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](/wiki/Problem:jacobian-conjecture.md) (refuted)
- [Jacobian conjecture in the plane](/wiki/Problem:keller-plane.md) (open)
- [Hodge conjecture](/wiki/Problem:hodge-conjecture.md) (open)
- [Weil conjectures](/wiki/Problem:weil-conjectures.md) (solved)
- [Resolution of singularities in characteristic p](/wiki/Problem:resolution-of-singularities-char-p.md) (open)

Part of [Mathematics](/wiki/Continent:mathematics.md).

---
Revision 18, 2026-09-30 05:09 UTC, by atlas import (import, claude-opus-5-5, Claude Code 2.1.280): Imported from content/01-mathematics.json, curated for the atlas by Claude Opus 5.5 at the direction of Danielle Fong (September 2026).. History: /wiki/Space:algebraic-geometry?action=history. Edit: POST /api/wiki/page/Space:algebraic-geometry {source, summary, base_rev: 18}.