Related papers: Divisor class groups of double covers over project…

A degree $d$ genus $g$ cover of the complex projective line by a smooth irreducible curve $C$ yields a vector bundle on the projective line by pushforward of the structure sheaf. We classify the bundles that arise this way when $d = 6$.…

The purpose of this paper is to study the structure of reflexive sheaves over projective spaces through hyperplane sections. We give a criterion for a reflexive sheaf to split into a direct sum of line bundles. An application to the theory…

A degree $d$ genus $g$ cover of the complex projective line by a smooth irreducible curve $C$ yields a vector bundle on the projective line by pushforward of the structure sheaf. We classify the bundles that arise this way when $d = 5$.…

Let $X$ be a projective manifold of dimension $n$. Suppose that $T_X$ contains an ample subsheaf. We show that $X$ is isomorphic to $\mathbb{P}^n$. As an application, we derive the classification of projective manifolds containing a…

For a double solid $V\to P_3(C)$ branched over a surface $B\subset P_3(C)$ with only ordinary nodes as singularities, we give a set of generators of the divisor class group $Pic(\tilde{V}})$ in terms of contact surfaces of $B$ with only…

It is proved that any strictly exceptional collection generating the derived category of coherent sheaves on a smooth projective variety X with \rk K_0(X) = \dim X + 1 constists of locally free sheaves up to a common shift.

We provide a splitting criterion for supervector bundles over the projective superspaces $\mathbb{P}^{n|m}$. More precisely, we prove that a rank $p|q$ supervector bundle on $\mathbb{P}^{n|m}$ with vanishing intermediate cohomology is…

As in algebraic geometry, an effective divisor class on a vertex-weighted graph is called special if also its residual class is effective. We study the question, when this is true already on the level of divisors; that is, when there exists…

For an affine double plane defined by an equation of the form z^2 = f, we study the divisor class group and the Brauer group. Two cases are considered. In the first case, f is a product of n linear forms in k[x,y] and X is birational to a…

We investigate the positivity and extension of invertible sheaves on group homogeneous spaces over coherent bases. Bypassing the failure of standard limit arguments and the classical Weil--Cartier correspondence, we develop a valuative…

Let $X\subset\mathbb P^{n+1}$ be a smooth complex projective hypersurface. In this paper we show that, if the degree of $X$ is large enough, then there exist global sections of the bundle of invariant jet differentials of order $n$ on $X$,…

We consider dual frames generated by actions of countable discrete groups on a Hilbert space. Module frames in a class of modules over a group algebra are shown to coincide with a class of ordinary frames in a representation of the group.…

We construct vector-valued modular forms on moduli spaces of curves and abelian varieties using effective divisors in projectivized Hodge bundles over moduli of curves. Cycle relations tell us the weight of these modular forms. In…

A plane curve on a the projective space over a field of characteristic zero is free if its associated sheaf T of tangent vector fields tangent is a free module. Relatively few free curves are known. Here we prove that a divisor consisting…

In the moduli space $\mathcal{R}_g$ of double \'etale covers of curves of a fixed genus $g$, the locus of covers of curves with a semicanonical pencil decomposes as the union of two divisors $\mathcal{T}^e_g$ and $\mathcal{T}^o_g$. Adapting…

We compute divisors class groups of singular surfaces. Most notably we produce an exact sequence that relates the Cartier divisors and almost Cartier divisors of a surface to the those of its normalization. This generalizes Hartshorne's…

We demonstrate how some classical computations of divisor class groups can be obtained using the theory of rational coefficient Weil divisors and related results of Watanabe.

In this article, we prove that any smooth projective variety $X$ which is a double cover of the projective space $\mathbb{P}^n$ ($n\geq 2$) admits an Ulrich bundle. When $n=2$, we show that on any such $X$, there is an Ulrich bundle of rank…

The derived category of bounded complexes of coherent sheaves is one of the most important algebraic invariants of a smooth projective variety. An important approach to understand derived categories is to construct full strongly exceptional…

For a smooth projective variety $X\subseteq \mathbb P^N$ over an algebraically closed field of char $0$, we show that the discriminant locus of a generic projection of $X$ is projectively dual to a general linear section of the dual…