Varieties
- Abelian Scheme
- Abelian Variety
- Abelian Variety Polarization
- Abelianity Conjecture
- Abhyankar-Sathaye Conjecture
- Affine Coordinates
- Affine Scheme
- Affine Variety
- Albanese Variety
- Algebraic Blow-Up
- Algebraic Correspondence
- Algebraic Cycle
- Algebraic Group
- Algebraic Normalization
- Algebraic Set
- Algebraic Torus
- Algebraic Variety
- Amoeba
- Ample Line Bundle
- Amplituhedron
- Anticanonical Linear System
- Anticanonical Nonvanishing Conjecture
- b-Divisor
- b-Semiampleness Conjecture
- Base Change
- Beauville-Bogomolov-Fujiki Form
- Birational Morphism
- Birkhoff's Theorem
- Bloch Conjecture
- Blow-Up Center
- Bogomolov-Gieseker Inequality
- Bogomolov Sheaf
- Bounded Klt Complement Conjecture
- Brauer-Severi Variety
- Bridgeland Stability Condition
- Burkhardt Quartic
- Calabi-Yau Variety
- Campana-Peternell Conjecture
- Canonical Bundle Formula
- Canonical Divisor
- Canonical Nonvanishing Conjecture
- Cartier Divisor
- Character Variety
- Chow Coordinates
- Chow Group
- Chow Ring
- Chow Variety
- Class VII Surface
- Closed Immersion
- Closed Subscheme
- Coamoeba
- Coherent Sheaf
- Complete Intersection
- Complete Linear System
- Conductor Ideal
- Coordinate Polynomial
- Coordinate Ring
- Coulomb Branch
- Cubic Fourfold
- Cycle
- Decomposition of the Diagonal
- Diagonal Complete Intersection
- Diagonal Morphism
- Divisor Complement
- Divisorial Log Terminal Pair
- Dual Abelian Variety
- Effective Cartier Divisor
- Equivariant Euler Characteristic
- Equivariant Line Bundle
- Étale Fundamental Group
- Étale Morphism
- Exceptional Divisor
- Fano Contraction
- Fano Index
- Fano Manifold
- Fano Pseudoindex
- Fano Type Contraction
- Fano Type Variety
- Fiber Product
- Flat Morphism
- Flip
- Fujita Freeness Conjecture
- Gauss-Manin Connection
- Generalized Abundance Conjecture
- Generalized Hodge Conjecture
- Generalized Kummer Variety
- Generalized Mukai Conjecture
- Generalized Pair
- Geometric Genus
- Geometric Langlands Correspondence
- Geometrically Regular Scheme
- Gepner-Type Stability Condition
- Global Nilpotent Cone
- Global Spherical Shell Conjecture
- Good Reduction
- Gromov-Witten Invariant
- Harder-Narasimhan Filtration
- Hasse's Conjecture
- Hecke Eigensheaf
- Higgs Bundle
- Hikita Conjecture
- Hilbert's Nullstellensatz
- Hitchin Fibration
- Hodge Circle
- Hodge Conjecture
- Hodge Cycle
- Hodge Group
- Hodge Structure
- Ideal Sheaf
- Iitaka Conjecture
- Iitaka Dimension
- Iitaka Fibration
- Invertible Sheaf
- Irreducible Component
- Irreducible Holomorphic Symplectic Manifold
- Irreducible Variety
- Jacobian Variety
- Kawamata Log Terminal Pair
- Kernel Sheaf
- Kobayashi Canonical-Ampleness Conjecture
- Kodaira Dimension
- Kollár-Pardon Conjecture
- Kuga-Satake Correspondence
- Kuznetsov Component
- Kuznetsov Rationality Conjecture
- Lagrangian Fibration
- Large Fundamental Group
- Large-Volume Stability Condition
- Lefschetz Standard Conjecture
- Lipman-Zariski Conjecture
- Lisse Sheaf
- Local System
- Locally Closed Subscheme
- Locally Finitely Presented Morphism
- Locally Noetherian Scheme
- Locally Ringed Space
- Log Abundance Conjecture
- Log Calabi-Yau Pair
- Log Canonical Pair
- Log Canonical Threshold
- Log Discrepancy
- Log Resolution
- Logarithmic Kodaira Dimension
- Milne's Rationality Conjecture
- Milnor Number
- Minimal Model Program
- Mixed Hodge Structure
- Moduli Space of Stable Curves
- Mori Fiber Space
- Morphism of Finite Type
- Multiplier Ideal
- Nagata-Biran-Szemberg Conjecture
- Nagata Conjecture
- Nakajima Quiver Variety
- Nef Divisor
- Nef Line Bundle
- Nef Vector Bundle
- Nilpotent Cone
- Nonabelian Hodge Correspondence
- Normal Variety
- Normalized Volume
- Numerical Dimension
- Open Immersion
- Open Subscheme
- p-adic Section Conjecture
- P=W Conjecture
- Perverse Leray Filtration
- Picard Number
- Picard Variety
- Pixton Completeness Conjecture
- Positive Geometry
- Principal Open Set
- Projection Morphism
- Projective Bundle
- Projective Line
- Projective Variety
- Proper Morphism
- Proper Subvariety
- Pseudo-Effective Divisor
- Q-Factorial Variety
- Quasi-Albanese Variety
- Quasiprojective Variety
- Quiver
- Quiver Representation
- Rational Curve
- Rational Equivalence
- Rational Homogeneous Variety
- Rational Map
- Rational Variety
- Rationally Connected Variety
- Reducible Variety
- Regular Scheme
- Resolution of Singularities
- Retract Rational Variety
- Scheme Immersion
- Schnell Fiber Space Conjecture
- Schubert Variety
- Semi-Log Canonical Pair
- Semiabelian Variety
- Semiample Divisor
- Seminormal Scheme
- Semipositive Line Bundle
- Separated Morphism
- Seshadri Constant
- Shafarevich Holomorphic Convexity Conjecture
- Sheaf Singular Support
- Siegel Moduli Variety
- Simple Normal Crossing Divisor
- Singular Variety
- Smooth Locus
- Smooth Morphism
- Smooth Variety
- Special Subvariety
- Special Variety
- Spherical Twist
- Stable Coordinate Conjecture
- Stable Curve
- Stably Rational Variety
- Stein Degree
- Strong Hyper-Kähler SYZ Conjecture
- Structure Morphism
- Subscheme
- Subvariety
- Symplectic Resolution
- Symplectic Singularity
- Tangent Cone
- Tangent Sheaf
- Tate Conjecture
- Tautological Ring
- Terminal Singularity
- Termination of Flips Conjecture
- Toric Variety
- Torsion Coset
- Tropical Geometry
- Universally Closed Morphism
- Unmixed
- Variation of Hodge Structure
- Virasoro Conjecture
- Weil Class
- Weil Conjectures
- Weil Divisor
- Zariski Cancellation Problem
- Zariski Multiplicity Conjecture
- Zilber-Pink Conjecture