We propose a variation of the notion of Segre class, by forcing a naive `inclusion-exclusion' principle to hold. The resulting class is computationally tractable, and is closely related to Chern-Schwartz-MacPherson classes. We deduce several general properties of the new class from this relation, and obtain an expression for the Milnor class of an arbitrary scheme in terms of this class.

This is a write-up of lectures presented at the first Arizona Winter School in Arithmetic Geometry on the abc conjecture. There isn’t anything new in these notes, except perhaps the point of view. Most of the results are in [V] and [TV]. The Brill-Segre formula counts the number of osculation points for a morphism of a curve to n-dimensional space and generalizes the Hurwitz formula (n = 1) and...

This paper generalizes work of Lascoux and Jo zeeak-Pragacz-Weyman computing the characteristic zero Betti numbers in minimal free resolutions of ideals generated by 2 2 minors of generic matrices and generic symmetric matrices, respectively. In the case of 2 2 minors, the quotients of certain polynomial rings by these ideals are the classical Segre and quadratic Veronese subalgebras, and we co...

We study virtual invariants of Quot schemes parametrizing quotients dimension at most 1 the trivial sheaf rank N on nonsingular projective surfaces. conjecture that generating series K-theoretic are given by rational functions. prove rationality for several geometries including punctual all smooth surfaces and X with p_g>0. also show cobordism classes can be irrational. Given a K-theory class r...

In this paper we introduce a new and large family of configurations whose toric ideals possess quadratic Gröbner bases. As an application, a generalization of algebras of Segre–Veronese type will be studied.

We express the Segre class of a monomial scheme in projective space in terms of log canonical thresholds of associated ideals. Explicit instances of the relation amount to identities involving the classical polygamma functions.