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Birational geometryComplete varietyHodge conjectureCorrespondenceField of definitionToric varietyProjective varietyFinite morphismAffine varietyCanonical bundleIntersection theoryAbelian varietyRational pointMorphism of algebraic varietiesModuli of algebraic curvesNoncommutative geometryMinimal model programProjective representationRelative homologyIsogenyAlgebraic elementHarmonic mapLocal fieldHilbert schemePlanarity testingRiemannian geometryComposition algebraSymplectic vector spaceAdjunction formulaSupersingular elliptic curveAlgebraic number fieldContact geometryLefschetz hyperplane theoremHolomorphic vector bundleModuli spaceIrreducible representationDirichlet problemSegre embeddingPoint in polygonAlgebraic varietySubgraph isomorphism problemHilbert projection theoremNormal schemeMultilinear formInvariant subspaceFundamental representationAffine groupCotangent bundleAlgebraic groupSymplectic geometryCongruenceAlgebraically closed fieldSymplectic manifoldAlgebraic torusDivisorGraph isomorphism problemSubmanifoldDual systemEquivariant cohomologyHamiltonian path problemAlgebraic closureClass field theoryEuler classChow groupSpin structureSplitting fieldHolonomic basisSemisimple lie algebraSymmetric bilinear formReflexive spaceInscribed square problemPetrov classificationIsotropic quadratic formMinkowski spaceHomographySymmetric spacePartition problemNoncommutative algebraic geometryEigenvalue perturbationFundamental groupPolygon triangulationDual spaceAlgebraic function fieldDegenerate bilinear formBilinear formDel pezzo surfaceSingular solutionGlobal analysisOrder topologyGauss circle problemCauchy problemGeneralized flag varietyDivision algebraSpectrum of a ringBorel subgroupCharacteristic polynomialInitial and terminal objectsGeometric group theoryResolvent formalismSmallest-circle problem