Related papers: Intersection Poincare polynomial for Nagaraj-Sesha…

We construct a weak categorification of the quantum toroidal algebra action on the Grothendieck group of moduli space of stable (or framed) sheaves over an algebraic surface, which is constructed by Schiffmann-Vasserot and Negu\c{t}. The…

We generalize the construction of a moduli space of semistable pairs parametrizing isomorphism classes of morphisms from a fixed coherent sheaf to any sheaf with fixed Hilbert polynomial under a notion of stability to the case of projective…

Consider the moduli space of framed flat $U(2)$ connections with fixed odd determinant over a surface. Newstead combined some fundamental facts about this moduli space with the Mayer-Vietoris sequence to compute its betti numbers over any…

We construct moduli stacks of stable sheaves for surfaces fibered over marked nodal curves by using expanded degenerations. These moduli stacks carry a virtual class and therefore give rise to enumerative invariants. In the case of a…

In this paper, we introduce modular polynomials for the congruence subgroup $\Gamma_0(M)$ when $ X_0(M) $ has genus zero and therefore the polynomials are defined by a Hauptmodul of $ X_0(M) $. We show that the intersection number of two…

Let $C$ be a smooth curve. In this paper we investigate the geometric properties of the double nested Hilbert scheme of points on $C$, a moduli space introduced by the third author in the context of BPS invariants of local curves and sheaf…

We compute moduli spaces of Bridgeland stable objects on an irreducible principally polarized complex abelian surface corresponding to twisted ideal sheaves. We use Fourier-Mukai techniques to extend the ideas of Arcara and Bertram to…

Fix a Chern character of a stable sheaf on the plane. Assume either the rank is at most 6 or the rank and first Chern class are coprime and the discriminant is sufficiently large. We use recent results of Bayer and Macri on Bridgeland…

Using several numerical invariants, we study a partition of the space of line arrangements in the complex projective plane, given by the intersection lattice types. We offer also a new characterization of the free plane curves using the…

For any moduli space of stable representations of quivers, certain smooth varieties, compactifying projective space fibrations over the moduli space, are constructed. The boundary of this compactification is analyzed. Explicit formulas for…

We prove that the weight-two Hodge structure of moduli spaces of torsion-free sheaves on a K3 surface is as described by Mukai (the rank is arbitrary but we assume the first Chern class is primitive). We prove the moduli space is an…

We find locally free resolutions of length one for all semi-stable sheaves supported on curves of multiplicity five in the complex projective plane. In some cases we also find geometric descriptions of these sheaves by means of extensions.…

A procedure resolving a torsion-free coherent sheaf on a nonsingular $N$-dimensional projective algebraic variety into a locally free sheaf on a projective scheme of certain class is proposed. This is a higher-dimensional analog of the…

In this paper, we construct toric data of moduli space of quasi maps of degree $d$ from P^{1} with two marked points to weighted projective space P(1.1,1,3). With this result, we prove that the moduli space is a compact toric orbifold. We…

When $k<n$, we study the coherent systems that come from a BGN extension in which the quotient bundle is strictly semistable. In this case we describe a stratification of the moduli space of coherent systems. We also describe the strata as…

We study the wall-crossing of the moduli spaces $\mathbf{M}^\alpha (d,1)$ of $\alpha$-stable pairs with linear Hilbert polynomial $dm+1$ on the projective plane $\mathbb{P}^2$ as we alter the parameter $\alpha$. When $d$ is 4 and 5, at each…

We determined the Picard group of the moduli of rank two stable sheaves on an arbitrary algebraic surface up to finite index

This is a note on calculating intersection numbers on moduli spaces of curves. A codimension 3 relation among tautological classes on the moduli space of genus 4 curves is given.

We show that each of the irreducible components of moduli of rank 2 torsion-free sheaves with odd Euler characteristic over a reducible nodal curve is rational.

We notice that for $0<d\le 6$ the Poincar\'e polynomial of Simpson moduli space $M_{dm + 1}(\mathbb P_2)$ is divisible by the Poincar\'e polynomial of the projective space $\mathbb P_{3d-1}$. A somehow regular behaviour of the difference of…