Related papers: Smooth correspondences between quiver varieties

We prove a formula which relates Euler characteristic of moduli spaces of stable pairs on local K3 surfaces to counting invariants of semistable sheaves on them. Our formula generalizes Kawai-Yoshioka's formula for stable pairs with…

Moduli spaces of stable sheaves on smooth projective surfaces are in general singular. Nonetheless, they carry a virtual class, which -- in analogy with the classical case of Hilbert schemes of points -- can be used to define intersection…

We unify problems about the equivariant geometry of symmetric quiver representation varieties, in the finite type setting, with the corresponding problems for symmetric varieties $GL(n)/K$ where $K$ is an orthogonal or symplectic group. In…

The so-called Hitchin-Kobayashi correspondence, proved by Donaldson, Uhlenbeck and Yau, establishes that an indecomposable holomorphic vector bundle over a compact Kahler manifold admits a Hermitian-Einstein metric if and only if the bundle…

We discuss the parabolic Hilbert scheme of points on smooth surface, which is an interesting generalization of Hilbert scheme of points on surface. Some of the studies by Ellingsrud-Stromme, Goettsche, Cheah, Nakajima and Grojnowski can be…

For a variety $X$ separated over a perfect field of characteristic $p>0$ which admits an embedding into a smooth variety, we establish an anti-equivalence between the bounded derived categories of Cartier crystals on $X$ and constructible…

We study the moduli space of twisted quasimaps from a fixed smooth projective curve to a Nakajima's quiver variety and the moduli space of $\delta$-stable framed twisted quiver bundles with moment map relations. We show that they carry…

The geometry of divisors on algebraic curves has been studied extensively over the years. The foundational results of this Brill-Noether theory imply that on a general curve, the spaces parametrizing linear series (of fixed degree and…

To a quiver $Q$ and choices of nonzero scalars $q_i$, non-negative integers $\alpha_i$, and integers $\theta_i$ labeling each vertex $i$, Crawley-Boevey--Shaw associate a "multiplicative quiver variety" $\mathcal{M}_\theta^q(\alpha)$, a…

We introduce a smooth mapping of some discrete space-time symmetries into quasi-continuous ones. Such transformations are related with q-deformations of the dilations of the Euclidean space and with the non-commutative space. We work out…

Let S be a ruled surface without sections of negative self-intersection. We classify the irreducible components of the moduli stack of torsion-free sheaves of rank 2 sheaves on S. We also classify the irreducible components of the…

We review the theory of quiver bundles over a K\"ahler manifold, and then introduce the concept of generalized quiver bundles for an arbitrary reductive group G. We first study the case when G=O(V) or Sp(V), interpreting them as orthogonal…

For algebraic varieties defined by hyperkahler or, more generally, algebraic symplectic reduction, it is a long-standing question whether the "hyperkahler Kirwan map" on cohomology is surjective. We resolve this question in the affirmative…

The Hilbert scheme $X^{[3]}$ of length-$3$ subschemes of a smooth projective variety $X$ is known to be smooth and projective. We investigate whether the property of having a multiplicative Chow-Kuenneth decomposition is stable under taking…

In this article, we classify the irreducible components of moduli stacks of torsion free sheaves of rank 2 on K3 surfaces of Picard number 1. For ruled surfaces, the components of moduli stacks of torsion free sheaves were classified by…

To each triangulation of any surface with marked points on the boundary and orbifold points of order three, we associate a quiver (with loops) with potential whose Jacobian algebra is finite dimensional and gentle. We study the stability…

A new construction is presented of scalar-flat Kaehler metrics on non-minimal ruled surfaces. The method is based on the resolution of singularities of orbifold ruled surfaces which are closely related to rank-2 parabolically stable…

We present results indicating that the decomposition of a Ricci-flat manifold in its irreducible factors is reflected by the derived category of coherent sheaves. More precisely, we prove that a smooth projective variety that is derived…

We give conceptual and combinatorial criteria for the normality and Cohen--Macaulayness of unions of Ekedahl--Oort strata in the special fiber of abelian type Shimura varieties. For unions of two strata, one of the two having codimension…

We study projective models of generalized Kummer fourfolds via O'Grady's theta groups and the classical Coble cubic. More precisely, we establish a duality between two singular models of the generalized Kummer fourfold of a Jacobian abelian…