Given that a projective variety X ⊂ ℙ n is an intersection of hypersurfaces, one of the most basic problems we can pose in relation to X is to describe the hypersurfaces that contain it. In particular, we want to know how many hypersurfaces of each degree contain X—that is, for each value of m, to know the dimension of the vector space of homogeneous polynomials of degree m vanishing on X.
KeywordsComplete Intersection Homogeneous Polynomial Projective Variety Betti Number Plane Curve
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