ClassInChowRing -- Gives the class of a hypersurface in the associated Chow ring of a product of projective spaces

Synopsis

• Usage:
ClassInToricChowRing(A,f)
• Inputs:
• A, , the Chow ring of \PP^{n_1} x...x\PP^{n_1}
• f, , an element of the coordinate ring of \PP^{n_1} x...x\PP^{n_1}
• Outputs:
• , the class of V(f), [V(f)] in the Chow ring of \PP^{n_1} x...x\PP^{n_1}

Description

This method finds the class [V(f)] of the hypersurface V(f) where f is a polynomial in the graded coordinate ring of \PP^{n_1} x...x\PP^{n_1}. The class [V(f)] is an element of the Chow ring of \PP^{n_1} x...x\PP^{n_1}. Consider \PP^3x\PP^4x\PP^1

 i1 : R=MultiProjCoordRing({3,4,1}) o1 = R o1 : PolynomialRing i2 : A=ChowRing(R) o2 = A o2 : QuotientRing i3 : f=random({1,1,1},R); i4 : ClassInChowRing(A,f) o4 = h + h + h 1 2 3 o4 : A

Ways to use ClassInChowRing :

• "ClassInChowRing(QuotientRing,RingElement)"

For the programmer

The object ClassInChowRing is .