Chern Classes of Logarithmic Vector Fields
نویسنده
چکیده
Let X be a nonsingular complex variety and D a reduced effective divisor in X. In this paper we study the conditions under which the formula cSM (1U ) = c(DerX(− logD)) ∩ [X] is true. We prove that this formula is equivalent to a RiemannRoch type of formula. As a corollary, we show that over a surface, the formula is true if and only if the Milnor number equals the Tjurina number at each singularity of D. We also show the Rimann-Roch type of formula is true if the Jacobian scheme of D is nonsingular or a complete intersection.
منابع مشابه
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