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--- status: draft
--- author(s): Popescu
--- notes:
document {
Key => tangentSheaf,
Headline => "tangent sheaf of a projective variety",
SeeAlso => {cotangentSheaf, sheaf,ProjectiveVariety}
}
document {
Key => {(tangentSheaf,ProjectiveVariety),[tangentSheaf,Minimize]},
Usage => "tangentSheaf X",
Inputs => {
"X",
Minimize => Boolean => {"whether to apply ", TO "minimalPresentation", " to the result before returning it"}
},
Outputs => {CoherentSheaf
},
"Computes the tangent sheaf of the projective variety ", TT "X",
PARA{},
"Tangent sheaf of the projective plane:",
EXAMPLE {
"P = Proj(QQ[a,b,c])",
"TP = tangentSheaf(P)",
"HH^0(TP(-1))",
"HH^1(TP(-3))"
},
"Tangent sheaf of a plane nodal and cuspidal curve:",
EXAMPLE {
"Node = Proj(QQ[a,b,c]/ideal(b^2*c-a^2*(a+c)))",
"Cusp = Proj(QQ[a,b,c]/ideal(b^2*c-a^3))",
"TNode = tangentSheaf(Node)",
"HH^0(TNode)",
"HH^1(TNode)",
"TCusp = tangentSheaf(Cusp)",
"HH^0(TCusp)",
"HH^1(TCusp)"
--- update this once we can compute the kernel of
--- a H^0(phi) for a sheaf map phi :F -> G
},
SeeAlso => {cotangentSheaf, sheaf,ProjectiveVariety}
}
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