Chern classes of logarithmic derivations for free divisors with Jacobian ideal of linear type
نویسندگان
چکیده
منابع مشابه
Chern Classes of Logarithmic Derivations for Free Divisors with Jacobian Ideal of Linear Type
Let X be a nonsingular variety defined over an algebraically closed field of characteristic 0, and D be a free divisor with Jacobian ideal of linear type. We compute the Chern class of the sheaf of logarithmic derivations along D and compare it with the Chern-Schwartz-MacPherson class of the hypersurface complement. Out result establishes a conjecture by Aluffi raised in [Alu12b].
متن کاملLinearity conditions on the Jacobian ideal and logarithmic–meromorphic comparison for free divisors
In this paper we survey the role of D-module theory in the comparison between logarithmic and meromorphic de Rham complexes of integrable logarithmic connections with respect to free divisors, and we present some new linearity conditions on the Jacobian ideal which arise in this setting. MSC: 32C38; 14F40; 32S40
متن کاملChern Classes of Logarithmic Vector Fields for Locally Quasi-homogeneous Free Divisors
Let X be a nonsingular complex projective variety and D a locally quasihomogeneous free divisor in X. In this paper we study a numerical relation between the Chern class of the sheaf of logarithmic derivations on X with respect to D, and the Chern-Schwartz-MacPherson class of the complement of D in X. Our result confirms a conjectural formula for these classes, at least after push-forward to pr...
متن کاملChern Classes of Logarithmic Vector Fields
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 singul...
متن کاملSplayed divisors and their Chern classes
We obtain several new characterizations of splayedness for divisors: a Leibniz property for ideals of singularity subschemes, the vanishing of a ‘splayedness’ module, and the requirements that certain natural morphisms of modules and sheaves of logarithmic derivations and logarithmic differentials be isomorphisms. We also consider the effect of splayedness on the Chern classes of sheaves of dif...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 2018
ISSN: 0025-5645
DOI: 10.2969/jmsj/76797679