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Macaulay2Doc :: euler(ProjectiveHilbertPolynomial)

euler(ProjectiveHilbertPolynomial) -- constant term of the Hilbert polynomial

Synopsis

Description

The command returns P(0) the constant term of P. This is also the Euler characteristic of the sheaf of rings of a projective variety with Hilbert polynomial P.

i1 : R = QQ[x_0..x_3]

o1 = R

o1 : PolynomialRing
i2 : C = Proj(R/monomialCurveIdeal(R, {1,3,4}));
i3 : P = hilbertPolynomial C

o3 = - 3*P  + 4*P
          0      1

o3 : ProjectiveHilbertPolynomial
i4 : euler P

o4 = 1

See also