Results 1 
6 of
6
Computing characteristic classes of projective schemes
 J. Symbolic Comput
, 2003
"... Abstract. We discuss an algorithm computing the pushforward to projective space of several classes associated to a (possibly singular, reducible, nonreduced) projective scheme. For example, the algorithm yields the topological Euler characteristic of the support of a projective scheme S, given the ..."
Abstract

Cited by 24 (10 self)
 Add to MetaCart
(Show Context)
Abstract. We discuss an algorithm computing the pushforward to projective space of several classes associated to a (possibly singular, reducible, nonreduced) projective scheme. For example, the algorithm yields the topological Euler characteristic of the support of a projective scheme S, given the homogeneous ideal of S. The algorithm has been implemented in Macaulay2. 1.
Equivariant Chern classes of singular algebraic varieties with group actions
"... Abstract. We define the equivariant ChernSchwartzMacPherson class of a possibly singular algebraic Gvariety over the base field C, or more generally over a field of characteristic 0. In fact, we construct a natural transforfrom the Gequivariant constructible function functor FG to the mation CG ..."
Abstract

Cited by 10 (1 self)
 Add to MetaCart
(Show Context)
Abstract. We define the equivariant ChernSchwartzMacPherson class of a possibly singular algebraic Gvariety over the base field C, or more generally over a field of characteristic 0. In fact, we construct a natural transforfrom the Gequivariant constructible function functor FG to the mation CG ∗ Gequivariant homology functor HG ∗ or AG ∗ (in the sense of TotaroEdidinGraham). This CG ∗ may be regarded as MacPherson’s transformation for (certain) quotient stacks. We discuss on other type Chern classes and applications. The VerdierRiemannRoch formula takes a key role throughout. 1.
Characteristic classes of singular varieties, Topics
 in Cohomological Studies of Algebraic Varieties (Ed. P. Pragacz), Trends in Mathematics, Birkhäuser
, 2005
"... Preface. These five lectures aim to explain an algebrogeometric approach to the study of different notions of Chern classes for singular varieties, with emphasis on results leading to concrete computations. The notes are organized so that every page deals with essentially one topic (a device which ..."
Abstract

Cited by 10 (0 self)
 Add to MetaCart
Preface. These five lectures aim to explain an algebrogeometric approach to the study of different notions of Chern classes for singular varieties, with emphasis on results leading to concrete computations. The notes are organized so that every page deals with essentially one topic (a device which I am borrowing from Marvin Minsky’s “The Society of Mind”). Every one of the five lectures consists of five pages. My main goal in the lectures was not to summarize the history or to give a complete, detailed treatment of the subject; five lectures would not suffice for this purpose, and I doubt I would be able to accomplish it in any amount of time anyway. My goal was simply to provide enough information so that interested listeners could start working out examples on their own. As these notes are little more than a transcript of my lectures, they are bound to suffer from the same limitations. In particular, I am certainly not quoting here all the sources that should be quoted; I offer my apologies to any author that may feel his or her contribution has been neglected. The lectures were given in the minischool with the same title organized by Pro
Euler characteristics of general linear sections and polynomial Chern classes
"... We obtain a precise relation between the ChernSchwartzMacPherson class of a subvariety of projective space and the Euler characteristics of its general linear sections. In the case of a hypersurface, this leads to simple proofs of formulas of DimcaPapadima and Huh for the degrees of the polar m ..."
Abstract

Cited by 8 (2 self)
 Add to MetaCart
We obtain a precise relation between the ChernSchwartzMacPherson class of a subvariety of projective space and the Euler characteristics of its general linear sections. In the case of a hypersurface, this leads to simple proofs of formulas of DimcaPapadima and Huh for the degrees of the polar map of a homogeneous polynomial, extending these formula to any algebraically closed field of characteristic 0, and proving a conjecture of Dolgachev on ‘homaloidal ’ polynomials in the same context. We generalize these formulas to subschemes of higher codimension in projective space. We also describe a simple approach to a theory of ‘polynomial Chern classes’ for varieties endowed with a morphism to projective space, recovering properties analogous to the DeligneGrothendieck axioms from basic properties of the Euler characteristic. We prove that the polynomial Chern class defines homomorphisms from suitable relative Grothendieck rings of varieties to Z[t].
On Milnor classes via invariants of singular subschemes
"... We derive a formula for the Milnor class of schemetheoretic global complete intersections (with arbitrary singularities) in a smooth variety in terms of the Segre class of its singular scheme. In codimension one the formula recovers a formula of Aluffi for the Milnor class of a hypersurface. Conten ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
We derive a formula for the Milnor class of schemetheoretic global complete intersections (with arbitrary singularities) in a smooth variety in terms of the Segre class of its singular scheme. In codimension one the formula recovers a formula of Aluffi for the Milnor class of a hypersurface. Contents
INCLUSIONEXCLUSION AND SEGRE CLASSES, II
, 2002
"... Abstract. Considerations based on the known relation between different characteristic classes for singular hypersufaces suggest that a form of the ‘inclusionexclusion’ principle may hold for Segre classes. We formulate and prove such a principle for a notion closely related to Segre classes. This is ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. Considerations based on the known relation between different characteristic classes for singular hypersufaces suggest that a form of the ‘inclusionexclusion’ principle may hold for Segre classes. We formulate and prove such a principle for a notion closely related to Segre classes. This is used to provide a simple computation of the classes introduced in [Alu], in certain special (but representative) cases. 1.