Related papers: Inflectional loci of scrolls

We study foliations by curves on the three-dimensional projective space with no isolated singularities, which is equivalent to assuming that the conormal sheaf is locally free. We provide a classification of the topological and algebraic…

Let $k$ be an algebraically closed field with characteristic $2$, and let $X$ be a smooth projective algebraic curve of genus $g \geqslant 2$ over $k$. Let $\mathcal{M}^s_X(2,\mathcal{L})$ be the moduli space of rank $2$ stable vector…

The general construction of self-adjoint configuration space representations of the Heisenberg algebra over an arbitrary manifold is considered. All such inequivalent representations are parametrised in terms of the topology classes of flat…

We extend the notion of absolute subsets of Betti moduli spaces of smooth algebraic varieties to the case of normal varieties. As a consequence we prove that twisted cohomology jump loci in rank one over a normal variety are a finite union…

Let X be a smooth irreducible complex projective curve of genus g > 1. In this paper, we give necessary and sufficient conditions for an unstable bundle of HN-lenght 2 to have a particular algebra of endomorphisms. Then, fixing the…

We compute the stable cohomology of moduli spaces of hyperelliptic curves of a fixed genus embedded on a fixed Hirzebruch surface. We also describe these moduli spaces of embedded hyperelliptic curves in terms of moduli spaces of pointed…

Let ($M$, $\Omega$) be a smooth symplectic manifold and $f:M\rightarrow M$ be a symplectic diffeomorphism of class $C^l$ ($l\geq 3$). Let $N$ be a compact submanifold of $M$ which is boundaryless and normally hyperbolic for $f$. We suppose…

In this paper, we study certain moduli spaces of vector bundles on the blowup of the projective plane in at least 10 very general points. Moduli spaces of sheaves on general type surfaces may be nonreduced, reducible and even disconnected.…

We survey the cohomology jumping loci and the Alexander-type invariants associated to a space, or to its fundamental group. Though most of the material is expository, we provide new examples and applications, which in turn raise several…

Let $\pi: X \longrightarrow C$ be a fibration with reduced fibers over a curve $C$ and consider a polarization $H$ on the surface $X$. Let $E$ be a stable vector bundle of rank $2$ on $C$. We prove that the pullback $\pi^*E$ is a $H-$stable…

The purpose of this paper is to define and study systematically some asymptotic invariants associated to base loci of line bundles on smooth projective varieties. We distinguish an open dense subset of the real big cone, called the stable…

Let $X$ be a smooth irreducible projective curve of genus $g$ and gonality 4. We show that the canonical model of $X$ is contained in a uniquely defined surface, ruled by conics, whose geometry is deeply related to that of $X$. This surface…

In the present note we study some arrangements of inflectional lines, hyperosculating conics, and a nodal plane cubic that are free. Moreover, we study weak combinatorics of arrangements consisting of lines, conics, and elliptic curves…

We find some equivalences of the derived category of coherent sheaves on a Gorenstein genus one curve that preserve the (semi)-stability of pure dimensional sheaves. Using them we establish new identifications between certain Simpson moduli…

Given two vector bundles E and F on a variety X and a morphism from Sym^2(E) to F, we compute the cohomology class of the locus in X where the kernel of this morphism contains a quadric of prescribed rank. Our formulas have many…

Let X be a geometrically connected smooth projective curve of genus one, defined over the field of real numbers, such that X does not have any real points. We classify the isomorphism classes of all stable real algebraic vector bundles over…

Using the moduli space of semiorthogonal decompositions in a smooth projective family, introduced by the second, the third and the fourth author, we propose a novel approach to indecomposability questions for derived categories. Modulo a…

The space of smooth genus 0 curves in projective space has a natural smooth compactification: the moduli space of stable maps, which may be seen as the generalization of the classical space of complete conics. In arbitrary genus, no such…

In this note we analyse the scrollar invariants of $k:1$ covers of $\mathbb P^1$ that factor through the normalisation of a nodal curve in the $m$-th Hirzebruch surface $\mathbb F_m$. We then give an existence theorem for nodal curves in…

Let X be a geometrically irreducible smooth projective curve over a field k. We describe the algebra of endomorphisms of indecomposable unstable vector bundles over X of rank 2 and degree d. Fixing some numerical invariants, namely the…