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We construct a conic bundle over an elliptic curve over a real quadratic field that is a counterexample to the Hasse principle not explained by the \'etale Brauer-Manin obstruction. We also give simple examples of threefolds with the same…
A degree $d$ genus $g$ cover of the complex projective line by a smooth curve $C$ yields a vector bundle on the projective line by pushforward of the structure sheaf. Which bundles are possible? Equivalently, which…
The aim of this paper is to give some characterizations for N-Legendre and N-slant curves in the unit tangent bundles of surfaces endowed with natural diagonal lifted structures.
We prove a criterion stating when a line bundle on a smooth coisotropic subvariety Y of a smooth variety X with an algebraic Poisson structure, admits a first order deformation quantization.
We describe when two multiprojective bundles (fibre products of projective bundles over the same base) over projective spaces are isomorphic as abstract varieties. We also describe when two relative symmetric powers of projective bundles…
We prove Kov\'acs' conjecture that claims that if the $p^{th}$ exterior power of the tangent bundle of a smooth complex projective variety contains the $p^{th}$ exterior power of an ample vector bundle then the variety is either projective…
We define and study a family of cubic surfaces in the projectivized tangent bundle over a four dimensional projective space associated to the root system D_5. The 27 lines are rational over the base and we determine the classifying map to…
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…
We show how quiver representations and their invariant theory natu- rally arise in the study of some moduli spaces parametrizing bundles dened on an algebraic curve, and how they lead to ne results regarding the geometry of these spaces.
In this note, we describe the structure of regular foliations with semi-positive anti-canonical bundle on smooth projective varieties.
We prove rigidity of various types of holomorphic parabolic geometry on smooth complex projective varieties.
We give a combinatorial classification of torus equivariant vector bundles on a (normal) projective T-variety of complexity-one. This extends the classification of equivariant line bundles on complexity-one T-varieties by Petersen-S\"uss on…
In this paper, we give a complete classification of initialized and ACM line bundles on a smooth quartic hypersurface on P^3$.
The aim of this paper is to find all algebraic threefolds admitting quasi-regular Poisson structure. There are three types of such varieties: abelian varieties, smooth flat conic bundles over abelian surfaces and quotients of the product of…
The present paper focuses on the study of the stable category of vector bundles for the weighted projective lines of weight triple. We find some important triangles in this category and use them to construct tilting objects with tubular…
In this article we prove new results on projective normality and normal presentation of adjunction bundle associated to an ample and globally generated line bundle on higher dimensional smooth projective varieties with nef canonical bundle.…
A complex orthogonal (geometric) structure on a complex manifold is a geometric structure locally modelled on a non-degenerate quadric. One of the first examples of such a structure on a compact manifold of dimension three was constructed…
We classify thick subcategories $\mathcal T \subset D^b(\mathrm{coh}\,C)$ for smooth projective curves $C$ over an algebraically closed field.
We consider characterizations of projective varieties in terms of their tangents. S. Mori established the characterization of projective spaces in arbitrary characteristic by ampleness of tangent bundles. J. Wahl characterized projective…
Let G be a semisimple connected linear algebraic group over C, and X a wonderful G-variety. We study the possibility of realizing X as a closed subvariety of the projective space of a simple G-module. We describe the wonderful varieties…