Related papers: Ansatz for $(-1)^{n-1}\nabla p_n$

For each elliptic curve A over the rational numbers we construct a 2-periodic S^1-equivariant cohomology theory E whose cohomology ring is the sheaf cohomology of A; the homology of the sphere of the representation z^n is the cohomology of…

We give an existence result on (H,A)-stable sheaves on a K3 or abelian surface X with primitive triple of invariants (rank,first Chern class,Euler characteristics) in the integral cohomology lattice. Such a result yields the existence of…

For a fixed 2-block Springer fiber, we describe the structure of its irreducible components and their relation to the Bialynicki-Birula paving, following work of Fung. That is, we consider the space of complete flags in C^n preserved by a…

For any closed complex manifold $X$, we calculate the Poincar\'{e} and Hodge polynomials of the delocalized equivariant cohomology $H^*(X^n, S_n)$ with a grading specified by physicists. As a consequence, we recover a special case of a…

For $n\ge 1$ we show that the length 1 nested Hilbert scheme of the total space $X_n$ of the line bundle $\mathcal O_{\mathbb P^1}(-n)$, parameterizing pairs of nested 0-cycles in $X_n$, is a quiver variety associated with a suitable quiver…

We expand the toolbox of (co)homological methods in computational topology by applying the concept of persistence to sheaf cohomology. Since sheaves (of modules) combine topological information with algebraic information, they allow for…

Let $X$ be a variety over a finite field. Given an order $R$ in a semi-simple algebra over the rationals and a constructible \'etale sheaf $F$ of $R$-modules over $X$, one can consider a natural non-commutative $L$-function associated with…

We revisit and give a detailed proof of a lemma of Okounkov showing that, for a scheme X with a torus action, the Euler characteristic generating function associated with a "factorisable" sequence of torus-equivariant coherent sheaves on…

We classify all Gieseker semi-stable sheaves on the complex projective plane that have dimension 1, multiplicity 6 and Euler characteristic 3. We show that their moduli space is birational to the blow-up at a special point of a certain…

We prove an identity relating the product of two opposite Schubert varieties in the (equivariant) quantum K-theory ring of a cominuscule flag variety to the minimal degree of a rational curve connecting the Schubert varieties. We deduce…

Various algebraic structures have recently appeared in a parallel way in the framework of Hilbert schemes of points on a surface and respectively in the framework of equivariant K-theory [N1,Gr,S2,W], but direct connections are yet to be…

Following Laumon [10], to a nonramified $\ell$-adic local system $E$ of rank $n$ on a curve $X$ one associates a complex of $\ell$-adic sheaves $_n{\cal K}_E$ on the moduli stack of rank $n$ vector bundles on $X$ with a section, which is…

We compute the cohomological Hall algebra of zero-dimensional sheaves on an arbitrary smooth quasi-projective surface $S$ with pure cohomology, deriving an explicit presentation by generators and relations. When $S$ has trivial canonical…

Given a semisimple element in the loop Lie algebra of a reductive group, we construct a quasi-coherent sheaf on a partial resolution of the trigonometric commuting variety of the Langlands dual group. The construction uses affine Springer…

Let S be a K3 surface. In part I of this paper, we constructed a representation of the group Aut D(S), of auto-equivalences of the derived category of S. We interpreted this infinite dimensional representation, as the natural action of Aut…

We introduce the notion of symmetric obstruction theory and study symmetric obstruction theories which are compatible with C*-actions. We prove that the contribution of an isolated fixed point under a C*-action to equivariant…

Let H_{ab} be the equivariant Hilbert scheme parametrizing the 0-dimensional subschemes of the affine plane invariant under the natural action of the one-dimensional torus T_{ab}:={(t^{-b},t^a), t\in k^*}. We compute the irreducible…

We prove the existence of an affine paving for the three-step flag Hilbert scheme $$ \text{Hilb}^{n, n+1, n+2}(0) := \left\{\mathbb{C}[[x,y]]\supset I_n\supset I_{n+1}\supset I_{n+2}: I_i \,\,\text{ ideals with } \text{dim}_{\mathbb{C}}…

Let $E$ be the bundle defined by applying a polynomial representation of $GL_n$ to the tautological bundle on the Hilbert scheme of $n$ points in the complex plane. By a result of Haiman, the Cech cohomology groups $H^i(E)$ vanish for all…

To a finite quiver equipped with a positive integer on each of its vertices, we associate a holomorphic symplectic manifold having some parameters. This coincides with Nakajima's quiver variety with no stability parameter/framing if the…