Related papers: Instanton sheaves on Fano threefolds

We describe the moduli space of SU(N) instantons in the presence of a general surface operator of type N=n_1+ ... +n_M in terms of the representations of the so-called chain-saw quiver, which allows us to write down the instanton partition…

In this paper we derive a list of all the possible indecomposable normalized rank--two vector bundles without intermediate cohomology on the prime Fano threefolds and on the complete intersection Calabi Yau threefolds, say $V$, of Picard…

We consider the structure of the derived categories of coherent sheaves on Fano threefolds with Picard number 1 and describe a strange relation between derived categories of different threefolds. In the Appendix we discuss how the ring of…

Adjusting conventional Chern-Simons theory to ${\rm G}_2$-manifolds, one describes ${\rm G}_2$-instantons on bundles over a certain class of $7$-dimensional flat tori which fiber non-trivially over $T^4$, by a pullback argument. Moreover,…

We study the geometry of the Fano schemes $\mathrm{\textbf{F}}_{k}(\mathrm{SD}_n^r)$ of the projective variety $\mathrm{SD}_n^r$ defined by the $r\times r$ minors of a symmetric $n\times n$ matrix filled with indeterminates. These schemes…

We study $H$-instanton bundles on the infinite family of smooth three-dimensional varieties $X_e=\mathbb{P}(\mathcal{O}_{\mathbb{P}^2} \oplus \mathcal{O}_{\mathbb{P}^2}(e))$, for $e \geq 0$. We provide two distinct monadic descriptions of…

We describe semiuniversal deformation spaces for the noncompact surfaces $Z_k := \operatorname{Tot} (\mathcal O_{\mathbb P^1} (-k))$ and prove that any nontrivial deformation $Z_k (\tau)$ of $Z_k$ is affine. It is known that the moduli…

We consider non-perturbative superpotentials from world-sheet instantons wrapped on holomorphic genus zero curves in heterotic string theory. These superpotential contributions feature prominently in moduli stabilization and large field…

Building on the work of Mukai, we explore the birational geometry of the moduli spaces M_{S,L} of semistable rank two torsion-free sheaves, with c_1=-K_S and c_2=2, on a polarized degree one del Pezzo surface (S,L); this is related to the…

Some coherent sheaves on projective varieties have a non reduced versal deformation space. For example, this is the case for most unstable rank 2 vector bundles on ${\mathbb P}_2$. In particular, it may happen that some moduli spaces of…

We prove that the space of mathematical instantons with second Chern class 5 over ${\mathbb P}_3$ is smooth and irreducible. Unified and simple proofs for the same statements in case of second Chern class $\leq 4$ are contained.

In the first part of this paper we provide a survey of some fundamental results about moduli spaces of framed sheaves on smooth projective surfaces. In particular, we outline a result by Bruzzo and Markushevich, and discuss a few…

In analogy with the Gopakumar-Vafa (GV) conjecture on Calabi-Yau (CY) 3-folds, Klemm and Pandharipande defined GV type invariants on Calabi-Yau 4-folds using Gromov-Witten theory and conjectured their integrality. In a joint work with…

Sheaves on non-reduced curves can appear in moduli space of 1-dimensional semistable sheaves over a surface, and moduli space of Higgs bundles as well. We estimate the dimension of the stack $\mathbf{M}_{X}(nC,\chi)$ of pure sheaves…

By using the classification of Fano 3-folds we prove: Let $X$ be Fano 3-fold. Assume that the tangent bundle $T_X$ of $X$ is not stable (i.e. semi-stable or unstable). Then $b_2\geq 2$ and a relative tangent sheaf $T_{X/Y}$ of a contraction…

We complete the classification of rank two affine manifolds in the moduli space of translation surfaces in genus three. Combined with a recent result of Mirzakhani and Wright, this completes the classification of higher rank affine…

We study the cohomology of reflexive rank 2 sheaves on smooth projective threefolds. Applications are given to the moduli space of reflexive sheaves.

Let X be a K3 surface of degree 8 in P^5 with hyperplane section H. We associate to it another K3 surface M which is a double cover of P^2 ramified on a sextic curve C. In the generic case when X is smooth and a complete intersection of…

In the case of the fine Simpson moduli spaces of 1-dimensional sheaves supported on plane quartics, the subvariety of sheaves that are not locally free on their support is connected, singular, and has codimension 2.

We study the large rank limit of the moduli spaces of framed bundles on the projective plane and the blown-up projective plane. These moduli spaces are identified with various instanton moduli spaces on the 4-sphere and $\cpbar $, the…