Related papers: Moduli of Very Ample Line Bundles

We show that there exists a fine moduli space for torsion-free sheaves on a projective surface, which have a "good framing" on a big and nef divisor. This moduli space is a quasi-projective scheme. This is accomplished by showing that such…

We propose an approach to study logarithmic sheaves T(-log A) associated with a hyperplane arrangements A on the projective space, based on projective duality, direct image functors and vector bundles methods. We focus on freeness of line…

In this paper we study Brill-Noether loci for rank-two vector bundles and describe the general member of some components as suitable extensions of line bundles.

We develop a new method for analyzing moduli problems related to the stack of pure coherent sheaves on a polarized family of projective schemes. It is an infinite-dimensional analogue of geometric invariant theory. We apply this to two…

Let $X$ be a smooth irreducible projective curve with an involution $\sigma$. A vector bundle $E$ over $X$ is called anti-invariant if there exists an isomorphism $\sigma^*E\rightarrow E^*$. In this paper, we give a construction of the…

Fix a ruled surface S obtained as the projective completion of a line bundle L on a complex elliptic curve; we study the moduli problem of parametrizing certain pairs consisting of a sheaf E on S and a map of E to a fixed reference sheaf on…

Let $M$ be a complete nonsingular fine moduli space of modules over an algebra $S$. A set of conditions is given for the Chow ring of $M$ to be generated by the Chern classes of certain universal bundles occurring in a projective resolution…

We survey recent progress in the study of moduli of vector bundles on higher-dimensional base manifolds. In particular, we discuss an algebro-geometric construction of an analogue for the Donaldson-Uhlenbeck compactification and explain how…

In this paper we give construct good moduli spaces for constructible sheaves and Stokes functors. Derived enhancement of such are also considered.

In this survey we provide an overview of some recent developments in the construction of moduli spaces using stack-theoretic techniques. We will also explain the analogue of Harder-Narasimhan stratifications for general stacks, known as…

We construct configuration spaces for cyclic covers of the projective line that admit extra automorphisms and we describe the locus of curves with given automorphism group. As an application we provide examples of arbitrary high genus that…

This is a review article exploring similarities between moduli of quiver representations and moduli of vector bundles over a smooth projective curve. After describing the basic properties of these moduli problems and constructions of their…

In arXiv:2407.11958, a moduli stack parametrizing $I$--indexed diagrams of Higgs bundles over a base stack $X$ was constructed for any finite simplicial set $I$, inspiring speculations about extending the non-Abelian Hodge correspondence to…

We describe weighted projective lines in the sense of Geigle and Lenzing by a moduli problem on the canonical algebra of Ringel. We then go on to study generators of the derived categories of coherent sheaves on the total spaces of their…

We resolve pathological wall-crossing phenomena for moduli spaces of sheaves on higher-dimensional base manifolds. This is achieved by considering slope-semistability with respect to movable curves rather than divisors. Moreover, given a…

We obtain effective results for the global generation of pluritheta line bundles on moduli spaces of vector bundles on curves. The main ingredient is an independent result giving an upper bound on the dimension of the Hilbert scheme of…

In this paper we construct certain moduli spaces, which we call moduli spaces of (principal) $F$-bundles, and study their basic properties. These spaces are associated to triples consisting of a smooth projective geometrically connected…

A procedure for computing the dimensions of the moduli spaces of reducible, holomorphic vector bundles on elliptically fibered Calabi-Yau threefolds X is presented. This procedure is applied to poly-stable rank n+m bundles of the form V +…

We consider some conditions under which a smooth projective variety X is actually the projective space. We also extend to the case of positive characteristic some results in the theory of vector bundle adjunction. We use methods and…

Given a covering f: X \to Y of projective manifolds, we consider the vector bundle E on Y given as the dual of f_*(\O_X) / \O_Y. This vector bundles often has positivity properties, e.g. E is ample when Y is projective space by a theorem of…