Mathlib Map

Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.RationalMap.comp

{X Y Z : AlgebraicGeometry.Scheme} →
  [PreirreducibleSpace ↥X] → [Nonempty ↥Y] → (f : X.RationalMap Y) → [f.IsDominant] → Y.RationalMap Z → X.RationalMap Z

Composition of rational maps. Requires f to be dominant, so that we may choose a dominant representative.

Defined in
Mathlib.AlgebraicGeometry.Birational.Composition
Cited by
7 results in Mathlib
Foundations
Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PreirreducibleSpaceNonemptyAlgebraicGeometry.Scheme.RationalMap.IsDominant
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicGeometry.Scheme.RationalMap.comp_def · cited by 2RationalMap.comp_defAlgebraicGeometry.Scheme.RationalMap.toRationalMap_comp · cited by 1RationalMap.toRationalMap…AlgebraicGeometry.Scheme.RationalMap.comp.congr_simp · cited by 0comp.congr_simpAlgebraicGeometry.Scheme.RationalMap.comp_assoc · cited by 0RationalMap.comp_assocAlgebraicGeometry.Scheme.RationalMap.comp_id · cited by 0RationalMap.comp_idAlgebraicGeometry.Scheme.RationalMap.comp_toRationalMap · cited by 0RationalMap.comp_toRation…AlgebraicGeometry.Scheme.RationalMap.id_comp · cited by 0RationalMap.id_compTopCat.carrier · cited by 3184TopCat.carrierAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCommRingCat · cited by 2333CommRingCatAlgebraicGeometry.PresheafedSpace.carrier · cited by 2020PresheafedSpace.carrierAlgebraicGeometry.SheafedSpace.toPresheafedSpace · cited by 1988SheafedSpace.toPresheafed…AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace · cited by 1892LocallyRingedSpace.toShea…AlgebraicGeometry.Scheme.toLocallyRingedSpace · cited by 1734Scheme.toLocallyRingedSpa…AlgebraicGeometry.Scheme.PartialMap · cited by 76Scheme.PartialMapPreirreducibleSpace · cited by 33PreirreducibleSpaceAlgebraicGeometry.Scheme.PartialMap.toRationalMap · cited by 26PartialMap.toRationalMapAlgebraicGeometry.Scheme.RationalMap · cited by 25Scheme.RationalMapAlgebraicGeometry.Scheme.PartialMap.comp · cited by 15PartialMap.compAlgebraicGeometry.Scheme.RationalMap.IsDominant · cited by 8RationalMap.IsDominantAlgebraicGeometry.Scheme.RationalMap.representative · cited by 7RationalMap.representativeRationalMap.compCITED BYCITES

Cites14

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Cited by7

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