Related papers: Conic bundles and iterated root stacks

We investigate stratified-algebraic vector bundles on a real algebraic variety X. A stratification of X is a finite collection of pairwise disjoint, Zariski locally closed subvarieties whose union is X. A topological vector bundle on X is…

We show that the Atiyah-Hirzebruch K-theory of spaces admits a canonical generalization for stratified spaces. For this we study algebraic constructions on stratified vector bundles. In particular the tangent bundle of a stratified manifold…

We construct a smooth algebraic stack of tuples consisting of genus two nodal curves, simple effective divisors away from the nodes, and twisted fields. It provides a desingularization of the moduli of genus two stable maps to projective…

We systematically study the moduli theory of symplectic varieties (in the sense of Beauville) which admit a resolution by an irreducible symplectic manifold. In particular, we prove an analog of Verbitsky's global Torelli theorem for the…

Let $X$ be a general conic bundle over the projective plane with branch curve of degree at least 19. We prove that there is no normal projective variety $Y$ that is birational to $X$ and such that some multiple of its anticanonical divisor…

A Central Limit Theorem is proved for linear random fields when sums are taken over finite disjoint union of rectangles. The approach does not rely upon the use of Beveridge Nelson decomposition and the conditions needed are similar to…

We establish the generalized canonical bundle formula for generalized lc-trivial fibrations with irrational coefficients over non-compact bases in the complex analytic setting, and we show that the discriminant b-divisor and moduli…

In 1957 Atiyah classified simple and indecomposable vector bundles on an elliptic curve. In this article we generalize his classification by describing the simple vector bundles on all reduced plane cubic curves. Our main result states that…

The space of unitary local systems of rank one on the complement of an arbitrary divisor in a complex projective algebraic variety can be described in terms of parabolic line bundles. We show that multiplier ideals provide natural…

In this paper, we investigate the concepts of generalized twice differentiability and quadratic bundles of nonsmooth functions that have been very recently proposed by Rockafellar in the framework of second-order variational analysis. These…

This article presents a theory of modules with iterative connection. This theory is a generalisation of the theory of modules with connection in characteristic zero to modules over rings of arbitrary characteristic. We show that these…

We study the existence and regularity of invariant graphs for bundle maps (or bundle correspondences with generating bundle maps motivated by ill-posed differential equations) having some relative partial hyperbolicity on non-trivial and…

We classify nets of conics in Desarguesian projective planes over finite fields of odd order, namely, two-dimensional linear systems of conics containing a repeated line. Our proof is geometric in the sense that we solve the equivalent…

We prove a Chekanov-type theorem for the spherization of the cotangent bundle $ST^*B$ of a closed manifold $B$. It claims that for Legendrian submanifolds in $ST^*B$ the property "to be given by a generating family quadratic at infinity"…

In this paper, it is proved that certain stable rank-3 vector bundles can be written as extensions of line bundles and stable rank-2 bundles. As an application, we show the rationality of certain moduli spaces of stable rank-3 bundles over…

We classify all positive integers n and r such that (stably) non-rational complex r-fold quadric bundles over rational n-folds exist. We show in particular that for any n and r, a wide class of smooth r-fold quadric bundles over projective…

By analyzing degeneracy loci over projectivized vector bundles, we recompute the degree of the discriminant locus of a vector bundle and provide a new proof of the Bogomolov instability theorem.

In this work, families of kinks are analytically identified in multifield theories with either polynomial or deformed sine-Gordon-type potentials. The underlying procedure not only allows us to obtain analytical solutions for these models,…

We present an open-closed topological quantum field theory for inverse monoids which generalizes the theory of principle fiber bundles with finite gauge group over Riemann surfaces with boundary. The theory is constructed using the…

Given a projective morphism of compact, complex, algebraic varieties and a relatively ample line bundle on the domain we prove that a suitable choice, dictated by the line bundle, of the decomposition isomorphism of the Decomposition…