Tangent Algebras
نویسندگان
چکیده
We study the Zariski tangent cone TX π −→ X to an affine variety X and the closure TX of π−1(Reg(X)) in TX . We focus on the comparison between TX and TX , giving sufficient conditions on X in order that TX = TX . One aspect of the results is to understand when this equality takes place in the presence of the reducedness of the Zariski tangent cone. Our other interest is to consider conditions on X in order that TX be normal or/and Cohen–Macaulay, and to prove that they are met by several classes of affine varieties including complete intersection, Cohen–Macaulay codimension two and Gorenstein codimension three singularities. In addition, when X is the affine cone over a smooth arithmetically normal Calabi–Yau projective variety, we establish when TX is also (the affine cone over) an arithmetically normal Calabi–Yau like (projective) variety. AMS 2000 Mathematics Subject Classification: Primary 13H10, 14F10; Secondary 14M05, 14M10.
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