Related papers: Moduli of sheaves on ribbons

We study the geometry of the moduli stack of vector bundles of fixed rank and degree over an algebraic curve by introducing a filtration made of open substacks build from $(k, l)$-stable vector bundles. $(k, l)$-stability was introduced by…

We construct the moduli space of r-jets at a point of Riemannian metrics on a smooth manifold. The construction is closely related to the problem of classification of jet metrics via differential invariants. The moduli space is proved to be…

Using an existence criterion for good moduli spaces of Artin stacks by Alper-Fedorchuk-Smyth we construct a proper moduli space of rank two sheaves with fixed Chern classes on a given complex projective manifold that are…

We develop a theory of quasimaps to a moduli space of sheaves $M$ on a surface $S$. Under some assumptions, we prove that moduli spaces of quasimaps are proper and carry a perfect obstruction theory. Moreover, they are naturally isomorphic…

In a previous article we introduced various moduli stacks of two-dimensional tamely potentially Barsotti-Tate representations of the absolute Galois group of a p-adic local field, as well as related moduli stacks of Breuil-Kisin modules…

A primitive multiple curve is a Cohen-Macaulay irreducible projective curve Y that can be locally embedded in a smooth surface, and such that C=Y_red is smooth. In this case, L=I_C/I_C^2 is a line bundle on C. If Y is of multiplicity 2,…

In this article we study the modular properties of a family of cyclic coverings of P^1 of degree N, in all odd characteristics. We compute the moduli space of the corresponding algebraic stack over Z[1/2], as well as the Picard groups over…

We systematically develop Bridgeland's and Bridgeland-Maciocia's techniques for studying elliptic fibrations, and identify criteria that ensure 2-term complexes are mapped to torsion-free sheaves under a Fourier-Mukai transform. As an…

This thesis contributes with a number of topics to the subject of string compactifications. In the first half of the work, I discuss the Hodge plot of Calabi-Yau threefolds realised as hypersurfaces in toric varieties. The intricate…

Consider an ample and globally generated line bundle $L$ on a smooth projective variety $X$ of dimension $N\geq 2$ over $\mathbb{C}$. Let $D$ be a smooth divisor in the complete linear system of $L$. We construct reflexive sheaves on $X$ by…

We compute the rational homology of the moduli stack $\mathcal{M}$ of objects in the derived category of certain smooth complex projective varieties $X$ including toric varieties, flag varieties, curves, surfaces, and some 3- and 4-folds.…

We present a novel notion of stable objects in a triangulated category. This Postnikov-stability is preserved by equivalences. We show that for the derived category of a projective variety this notion includes the case of semistable…

We construct moduli spaces of semistable objects on an Enriques surface for generic Bridgeland stability condition and prove their projectivity. We further generalize classical results about moduli spaces of semistable sheaves on an…

We study the moduli space of stable sheaves of Euler characteristic 1 supported on curves of bidegree (3, 3) contained in a smooth quadric surface. We show that this moduli space is rational. We compute its Betti numbers by studying the…

We show a few basic results about moduli spaces of semistable modules over Lie algebroids. The first result shows that such moduli spaces exist for relative projective morphisms of noetherian schemes, removing some earlier constraints. The…

We study noncompact Calabi-Yau threefolds, their moduli spaces of vector bundles and deformation theory. We present Calabi-Yau threefolds that have infinitely many distinct deformations, constructing them explicitily, and describe the…

We investigate the geometry of the Simpson moduli space M of stable sheaves on P_3 with Hilbert polynomial H(m)=3m+1 and describe explicitly the two smooth, rational components, their 11-dimensional smooth, transversal intersection and the…

We study locally Cohen-Macaulay curves of low degree in the Segre threefold with Picard number three and investigate the irreducible and connected components respectively of the Hilbert scheme of them. We also discuss the irreducibility of…

We study the tropicalization of the moduli space of algebraic spin curves, exhibit its combinatorial stratification and prove that the strata are irreducible. We construct the moduli space of tropical spin curves, prove that it is…

In this paper we study the relationship between three compactifications of the moduli space of Hermitian-Yang-Mills connections on a fixed Hermitian vector bundle over a projective algebraic manifold of arbitrary dimension. Via the…