Related papers: Residual intersection theory with reducible scheme…

Characteristic classes, which are abstract topological invariants associated with vector bundles, have become an important notion in modern physics with surprising real-world consequences. As a representative example, the incredible…

Using the Semple bundle construction, we derive an intersection-theoretic formula for the number of simultaneous contacts of specified orders between members of a generic family of degree $d$ plane curves and finitely many fixed curves. The…

Using raising operators and geometric arguments, we establish formulas for the K-theory classes of degeneracy loci in classical types. We also find new determinantal and Pfaffian expressions for classical cases considered by Giambelli: the…

We introduce the notion of residual intersections of modules and prove their existence. We show that projective dimension one modules have Cohen-Macaulay residual intersections, namely they satisfy the relevant Artin-Nagata property. We…

Let R be a discrete valuation ring with algebraically closed residue field, and consider a smooth curve CK over the field of fractions K. For any positive integer r prime to the residual characteristic, we consider the finite K-group scheme…

We give a new residual intersection decomposition for the refined intersection products of Fulton-MacPherson. Our formula refines the celebrated residual intersection formula of Fulton, Kleiman, Laksov, and MacPherson. The new decomposition…

We prove a closed formula for integrals of the cotangent line classes against the top Chern class of the Hodge bundle on the moduli space of stable pointed curves. These integrals are computed via relations obtained from virtual…

The theory of Q-Cartier divisors on the space of n-pointed, genus 0, stable maps to projective space is considered. Generators and Picard numbers are computed. A recursive algorithm computing all top intersection products of Q-Divisors is…

We present explicit formulas for the intersection pairing in the intersection cohomology of the moduli space $M_0(r)$ of rank-$r$, degree-$0$ semistable bundles on a Riemann surface. The key idea is to realize this intersection cohomology…

A degree $d$ genus $g$ cover of the complex projective line by a smooth irreducible curve $C$ yields a vector bundle on the projective line by pushforward of the structure sheaf. We classify the bundles that arise this way when $d = 5$.…

We introduce a general approach to traces that we consider as linear continuous functionals on some function space where we focus on some special choices for that space. This leads to an integral calculus for the computation of the precise…

We give a formula relating the total Tjurina number and the generic splitting type of the bundle of logarithmic vector fields associated to a reduced plane curve. By using it, we give a characterization of nearly free curves in terms of…

For a quasi-projective scheme M which carries a perfect obstruction theory, we construct the virtual cobordism class of M. If M is projective, we prove that the corresponding Chern numbers of the virtual cobordism class are given by…

A cocycle $\Omega: P \times G \to H$ taking values in a Lie group $H$ for a free right action of $G$ on $P$ defines a principal bundle $Q$ with the structure group $H$ over $P/G.$ The Chern character of a vector bundle associated to $Q$…

Let $E$ be a rank 2, degree $d$ vector bundle over a genus $g$ curve $C$. The loci of stable pairs on $E$ in class $2[C]$ fixed by the scaling action are expressed as products of $\Quot$ schemes. Using virtual localization, the stable pairs…

This is a continuation of "Rational families of vector bundles on curves, I". Let C be a smooth projective curve of genus at least 2 and let M be the moduli space of rank 2, stable vector bundles on C, with fixed determinant of degree 1.…

We give a sufficient criterion for the Chow or algebraic bordism groups of an algebraic stack, localized at a set of Chern classes of line bundles, to be concentrated in some closed substack. This is a vast generalization of the torus…

We study the relative Hilbert scheme of a family of nodal (or smooth) curves, over a base of arbitrary dimension, via its (birational) cycle map, going to the relative symmetric product. We show the cycle map is the blowing up of the…

We exhaustively classify topological equivariant complex vector bundles over two-torus under a compact Lie group (not necessarily effective) action. It is shown that inequivariant Chern classes and isotropy representations at (at most) six…

We classify equivariant topological complex vector bundles over real projective plane under a compact Lie group (not necessarily effective) action. It is shown that nonequivariant Chern classes and isotropy representations at (at most)…