Related papers: An exceptional locus in the perfect compactificati…

In this note, we study the $p$-complete topological cyclic homology of the affine line relative to a ring $A$ which is smooth over a perfectoid ring $R$. Denoting by $NTC(A; \mathbb{Z}_p)$ the spectrum which measures the failure of…

Let $G$ be a simple algebraic group of adjoint type over $\mathbb C$, and let $M$ be the wonderful compactification of a symmetric space $G/H$. Take a $\widetilde G$--equivariant principal $R$--bundle $E$ on $M$, where $R$ is a complex…

We characterize the exact lumpability of smooth vector fields on smooth manifolds. We derive necessary and sufficient conditions for lumpability and express them from four different perspectives, thus simplifying and generalizing various…

Consider all moduli points corresponding with polarized abelian varieties in characteristic p such that the associated quasi-polarized p-divisible group is geometrically isomorphic with a given one. This defines a subset C of the moduli…

We prove the bounded packing property for any abelian subgroup of a group acting properly and cocompactly on a CAT(0) cube complex. A main ingredient of the proof is a cubical flat torus theorem. This ingredient is also used to show that…

Let $V$ be a finite dimensional $k$-vector space, where $k$ is an algebraic closed field of characteristic zero. Let $G \subseteq \mathrm{SL}(V)$ be a finite abelian group, and denote by $S$ the $G$-invariant subring of the polynomial ring…

We give conditions under which natural lines bundles associated with completions of period mappings are semi-ample and ample.

For a vector bundle $\mathcal E \to \mathbb P^\ell$ we investigate exceptional sequences of line bundles on the total space of the projectivisation $X = \mathbb P(\mathcal E)$. In particular, we consider the case of the cotangent bundle of…

I prove the existence, and describe the structure, of moduli space of pairs $(p,\Theta)$ consisting of a projective variety $P$ with semiabelian group action and an ample Cartier divisor on it satisfying a few simple conditions. Every…

This article gives a classification, up to symplectic equivalence, of singular Lagrangian foliations given by a completely integrable system of a 4-dimensional symplectic manifold, in a full neighbourhood of a singular leaf of focus-focus…

In this note it is shown that associating to a principally polarized abelian variety its de Rham cohomology defines a faithfully flat morphism of the moduli space of principally polarized abelian varieties in positive characteristics to the…

For a given complex projective variety, the existence of entire curves is strongly constrained by the positivity properties of the cotangent bundle. The Green-Griffiths-Lang conjecture stipulates that entire curves drawn on a variety of…

Fix a smooth projective curve over a field of characteristic zero and a finite set of punctures. Let G be a connected linear algebraic group. We prove that the moduli of G-bundles with logarithmic connections having fixed residue classes at…

Our interest is a regularity of a minimal singular metric of a line bundle. One main conclusion of our general result in this paper is the existence of continuous Hermitian metrics with semi-positive curvatures on the so-called Zariski's…

Let $(X, \Delta)$ be a projective klt three dimensional pair defined over an algebraically closed field characteristic larger than 5. Let $L$ be a nef and big line bundle on $X$ such that $L-K_X-\Delta$ is big and nef. We show that $L$ is…

We show that positivity of the CM line associated to a family of polarised varieties is intimately related to the stability of its members. We prove that the CM line is nef on any curve which meets the stable locus, and that it is…

We introduce the abstract notion of a \emph{smoothable fine compactified Jacobian} of a nodal curve, and of a family of nodal curves whose general element is smooth. Then we introduce the notion of a combinatorial stability condition for…

We study the affine cone over a reducible nodal curve $X$ obtained by gluing three projective lines along three pairs of points to form a connected curve of arithmetic genus \(1\). We endow \(X\) with a line bundle \(L\) of multidegree…

In this paper, we study positive monad vector bundles on complete intersection Calabi-Yau manifolds in the context of E8 x E8 heterotic string compactifications. We show that the class of such bundles, subject to the heterotic anomaly…

The \emph{Bohr compactification} of an arbitrary topological group $G$ is defined as the group compactification $(bG,b)$ with the following universal property: for every continuous homomorphism $h$ from $G$ into a compact group $K$ there is…