Related papers: On Q-conic bundles

Given a complex projective manifold $X$ and a divisor $D$ with normal crossings, we say that the logarithmic tangent bundle $T_X(-\log D)$ is R-flat if its pull-back to the normalization of any rational curve contained in $X$ is the trivial…

We consider the moduli space of log smooth pairs formed by a cubic surface and an anticanonical divisor. We describe all compactifications of this moduli space which are constructed using Geometric Invariant Theory and the anticanonical…

For any almost-simple group $G$ over an algebraically closed field $k$ of characteristic zero, we describe the automorphism group of the moduli space of semistable $G$-bundles over a connected smooth projective curve $C$ of genus at least…

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 $d = 5$.…

We define the pull-back of a smooth principal fibre bundle, and show that it has a natural principal fibre bundle structure. Next, we analyse the relationship between pull-backs by homotopy equivalent maps. The main result of this article…

We study the existence problem and the enumeration problem for sections of Serre fibrations over compact orientable surfaces. When the fundamental group of the fiber is finite, a complete solution is given in terms of 2-dimensional…

Let $X$ be a smooth quartic hypersurface in $\mathbb{P}^3$. By the Brill-Noether theory of curves on K3 surfaces, if a rank 2 aCM bundle on $X$ is globally generated, then it is the Lazarsfeld-Mukai bundle $E_{C,Z}$ associated with a smooth…

Mumford defined a natural isomorphism between the intermediate jacobian of a conic-bundle over $P^2$ and the Prym variety of a naturally defined \'etale double cover of the discrminant curve of the conic-bundle. Clemens and Griffiths used…

We present three new inequalities tying the signature, the simplicial volume and the Euler characteristic of surface bundles over surfaces. Two of them are true for any surface bundle, while the third holds on a specific family of surface…

Let $k$ be an imperfect field. Let $X$ be a regular variety over $k$ and set $Y$ to be the normalization of $(X \times_k k^{1/p^{\infty}})_{{\rm red}}$. In this paper, we show that $K_Y+C=f^*K_X$ for some effective divisor $C$ on $Y$. We…

Let $k$ be a field with char $k \not= 2$, $X$ be an affine surface defined by the equation $z^2=P(x)y^2+Q(x)$ where $P(x), Q(x) \in k[x]$ are separable polynomials. We will investigate the rationality problem of $X$ in terms of the…

Let L --> X be a complex line bundle over a compact connected Riemann surface. We consider the abelian vortex equations on L when the metric on the surface has finitely many point degeneracies or conical singularities and the line bundle…

We study based one-dimensional modules of quantum symmetric pairs over the field $\mathbb{Q}(q)$. We provide a complete classification of one-dimensional $\mathbf{B}$-modules that appear as submodules of simple finite-dimensional based…

We study relations among characteristic classes of smooth manifold bundles with highly-connected fibers. For bundles with fiber the connected sum of $g$ copies of a product of spheres $S^d \times S^d$ and an odd $d$, we find numerous…

Let $X \subset \mathbb P^3$ be a nonsingular cubic hypersurface. Faenzi (\cite{F}) and later Pons-Llopis and Tonini (\cite{PLT}) have completely characterized ACM line bundles over $X$. As a natural continuation of their study in the…

We prove vanishing results for the generalized Miller-Morita-Mumford classes of some smooth bundles whose fiber is a closed manifold that supports a nonpositively curved Riemannian metric. We also find, under some extra conditions, that the…

We study ACM bundles on cubic fourfolds containing a plane exploiting the geometry of the associated quadric fibration and Kuznetsov's treatment of their bounded derived categories of coherent sheaves. More precisely, we recover the K3…

This work establishes a structure theorem for compact K\"ahler manifolds with semipositive anticanonical bundle. Up to finite \'etale cover, it is proved that such manifolds split holomorphically and isometrically as a product of Ricci flat…

We classify holomorphic as well as algebraic torus equivariant principal $G$-bundles over a nonsingular toric variety $X$, where $G$ is a complex linear algebraic group. It is shown that any such bundle over an affine, nonsingular toric…

A surface automorphism is strongly irreducible if every essential simple closed curve in the surface has nontrivial geometric intersection with its image. We show that a three-manifold admits only finitely many inequivalent surface bundle…