Math.RootLoci.Classic

Classical results:

• Hilbert's degree formula
• some enumarative geometry computations by Schubert

Documentation

codim :: Partition -> Int

Codimension of a strata. This is simply (sum mu_i) - length(mu).

dimension :: Partition -> Int

Dimension of the strata. dim = length(mu).

Hilbert formula

hilbert :: Partition -> Integer

Hilbert's formula for the degree of a stratum

hilbert2 :: Partition -> Integer

Hilbert's degree formula, another version (as a sanity test).

Enumerative geometry

degreeOfDualCurve :: Int -> Integer

The degree of the dual curve is d(d-1)

numberOfCurveFlexes :: Int -> Integer

Number of flex lines to a generic degree d plane curve

numberOfCurveBiTangents :: Int -> Integer

Number of bitangent lines to a generic degree d plane curve

numberOfSurface4xTangents :: Int -> Integer

Number of 4-tangent lines to a generic degree d surface (Schubert)

numberOfSurface5xHyperflexes :: Int -> Integer

Number of lines meeting a generic degree d surface at point with 5x multiplicity

bidegreeOfSurfaceBiTangents :: Int -> (Integer, Integer)

Bidegree of bitangent locus of a generic hypersurface

(See: Kathlen Kohn, Bernt Ivar Utstol Nodland, Paolo Tripoli: Secants, bitangents, and their congruences)

bidegreeOfSurfaceFlexes :: Int -> (Integer, Integer)

Bidegree of the flex locus of a generic hypersurface

(See: Kathlen Kohn, Bernt Ivar Utstol Nodland, Paolo Tripoli: Secants, bitangents, and their congruences)