Related papers: Subvarieties with q-ample normal bundle and q-ampl…

We prove new boundedness results across different areas of algebraic geometry, stemming from a unifying technical starting point: bounding the integer $q > 0$ such that the $q$-th Hodge bundle becomes (semi-)positive for families of stable…

Here we define the concept of $L$-regularity for coherent sheaves on the Grassmannian G(1,4) as a generalization of Castelnuovo-Mumford regularity on ${\bf{P}^n}$. In this setting we prove analogs of some classical properties. We use our…

We consider stable and semistable principal bundles over a smooth projective real algebraic curve, equipped with a real or pseudo-real structure in the sense of Atiyah. After fixing suitable topological invariants, one can build a suitable…

Recently McBreen and Webster constructed a tilting bundle on a smooth hypertoric variety (using reduction to finite characteristic) and showed that its endomorphism ring is Koszul. In this short note we present alternative proofs for these…

We study the following question: Given a vector bundle on a projective variety $X$ such that the restriction of $E$ to every closed curve $C \,\subset\, X$ is ample, under what conditions $E$ is ample? We first consider the case of an…

We translate some fundamental properties satisfied by topological principal bundles into the setting of Hopf-Galois extensions. The properties are: functoriality, homotopy, and triviality. The main new concept of the paper is the homotopy…

In this paper we study $F$-divided bundles on irreducible Noetherian normal $F$-finite $\mathbb{F}_p$-schemes and we show that their Tannakian category is governed by the behaviour at the generic point. In particular, if $U\subset X$ is an…

We introduce multi-uniformized stacks as a generalization of the Abramovich--Hassett construction of uniformized twisted varieties. We prove an equivalence between the category of multi $\mathbb{Q}$-line bundles satisfying an analogue of…

Let $X$ be a smooth projective variety acted on by a reductive group $G$. Let $L$ be a positive $G$-equivariant line bundle over $X$. We use the Witten deformation of the Dolbeault complex of $L$ to show, that the cohomology of the sheaf of…

We develop a generalized field space geometry for higher-derivative scalar field theories, expressing scattering amplitudes in terms of a covariant geometry on the all-order jet bundle. The incorporation of spacetime and field derivative…

The purpose of this note is to extend some classical results on quasi-projective schemes to the setting of derived algebraic geometry. Namely, we want to show that any vector bundle on a derived scheme admitting an ample line bundle can be…

Using results of Gathmann, we prove the following theorem: If a smooth projective variety X has generically semisimple (p,p)-quantum cohomology, then the same is true for the blow-up of X at any number of points. This a successful test for…

We consider those projective bundles (or Brauer-Severi varieties) over an abelian variety that are homogeneous, i.e., invariant under translation. We describe the structure of these bundles in terms of projective representations of…

We prove the existence theorem for basic elements in the quasi-projective case, extending results of Eisenbud-Evans and Bruns from the affine case. We give several geometric applications. For example, we show that every local complete…

We resolve an open problem posed by Alexeev-Knutson on the projectivity of the moduli of branchvarieties in the equidimensional case. As an application, we construct projective moduli spaces of reduced equidimensional varieties equipped…

We investigate the geometry of a normal bundle equipped with a $(p,q)$-metric, i.e., Riemannian metric of Cheeger-Gromoll type, to the submanifold of a Riemannian manifold. We derive all natural object as the Levi-Civita connection,…

We prove that in the varieties where every compact congruence is a factor congruence and every nontrivial algebra contains a minimal subalgebra, a finitely presented algebra is projective if and only if it has every minimal algebra as its…

For a smooth projective variety $X$ of dimension $d \geq 5$ over an algebraically closed field $k$ of characteristic zero, it is shown in this paper that the bounded derived category of the Hilbert scheme of three points $X^{[3]}$ admits a…

We introduce a class of $G$-invariant connections on a homogeneous principal bundle $Q$ over a hermitian symmetric space $M=G/K$. The parameter space carries the structure of normal variety and has a canonical anti-holomorphic involution.…

In this paper we examine different problems regarding complete intersection varieties of high degree in a complex projective space. First we show how one can deduce hyperbolicity for generic complete intersection of high multidegree and…