Related papers: A note on lc-trivial fibrations

Let C be a curve of genus g and L a line bundle of degree 2g on C . Let M be the kernel of the evaluation map from the trivial bundle with fibre H^0(C,L) into L . We show that when L is general enough, the rank g bundle M and its exterior…

Let $(X,B)$ be a complex projective klt pair, and let $f\colon X\to Z$ be a surjective morphism onto a normal projective variety with maximal albanese dimension such that $K_X+B$ is relatively big over $Z$. We show that such pairs have good…

We present here a method which allows to derive a nontrivial lower bounds for the least common multiple of some finite sequences of integers. We obtain efficient lower bounds (which in a way are optimal) for the arithmetic progressions and…

We study Lie foliations on compact manifolds, in case the Lie group is compact. Our main results improve Tischler classical result on the existence of fibration and, as an application, we study the case the manifold has an amenable…

Let $k$ be a number field and let $\pi \colon X \rightarrow \mathbb{P}_k^1$ be a smooth conic bundle. We show that if $X/k$ has four geometric singular fibers with $X(\mathbb{A}_k)\neq \emptyset$ or non-trivial Brauer group, then $X$…

Let $X$ be a smooth projective variety over the complex numbers, and $\Delta \subseteq X$ a reduced divisor with normal crossings. We present a slightly simplified proof for the following theorem of Campana and P\u{a}un: If some tensor…

We consider the integer point transform $\sigma _P (\mathbf{x}) = \sum _{\mathbf{m} \in P\cap \mathbb{Z}^n} \mathbf{x}^\mathbf{m} \in \mathbb C [x_1^{\pm 1},\ldots, x_n^{\pm 1}]$ of a polytope $P\subset \mathbb{R}^n$. We show that if $P$ is…

For which positive integers $n,k,r$ does there exist a linear $[n,k]$ code $C$ over $\mathbb{F}_q$ with all codeword weights divisible by $q^r$ and such that the columns of a generating matrix of $C$ are projectively distinct? The…

Cartan's magic formula L_X = i_X d + d i_X = (d+i_X)^2=D_X^2 relates the exterior derivative d, an interior derivative i_X and its Lie derivative L_X. We use this formula to define a finite dimensional vector space of vector fields X on a…

Let X ->Y be a Zariski locally trivial fibration of smooth complex projective varieties, with fiber F. We give a structure theorem for the derived category of X provided both F and Z have a full strongly exceptional collection of line…

In this note, we show that if $f\colon M\rightarrow X$ is a germ of a projective Lagrangian fibration from a holomorphic symplectic manifold $M$ onto a normal analytic variety $X$ with isolated quotient singularities, then $X$ is smooth. In…

The aim of this paper is to prove an important generalization of the construction of the Incidence Divisor given in [BMg]. Let Z be a complex manifold and (X_{s})_{s\in S}an family of n-cycles (not necessarily compact) in Z parametrized by…

Let $(X,L_{X})$ be an $n$-dimensional polarized manifold. Let $D$ be a smooth hypersurface defined by a holomorphic section of $L_{X}$. In this paper, we show the existence of a complete K\"{a}hler metric on $X \setminus D$ whose scalar…

Let C be a general connected, smooth, projective curve of positive genus g. For each nonnegative integer i we give formulas for the number of pairs (P,Q) em C x C off the diagonal such that (g+i-1)Q-(i+1)P is linearly equivalent to an…

We prove that for every compactum X with dim_Z X <= n >= 2 there is a cell-like resolution r: Z --> X from a compactum Z onto X such that dim Z <= n and for every integer k and every abelian group G such that dim_G X <= k >= 2 we have dim_G…

This work is the geometric part of our proof of the weighted fundamental lemma, which is an extension of Ng\^o Bao Ch\^au's proof of the Langlands-Shelstad fundamental lemma. Ng\^o's approach is based on a study of the elliptic part of the…

Let $k$ be a field of positive characteristic. We prove that the only linear relations between the Hodge numbers $h^{i,j}(X) = \dim H^j(X,\Omega_X^i)$ that hold for every smooth proper variety $X$ over $k$ are the ones given by Serre…

This paper generalizes the easy addition formula. Given a normal variety $X$ with an invertible sheaf $L$, inequalities are found bounding $\ka(X,L)$ from above based on the behavior of $L$ restricted to a subvariety or to a pair of…

In this paper, we study a sextic del Pezzo fibration over a curve comprehensively. We obtain certain formulae of several basic invariants of such a fibration. We also establish the embedding theorem of such a fibration which asserts that…

Necessary and sufficient conditions are given for a negative integer to be a trivial zero of a new type of $L$-series recently discovered by F. Pellarin, and it is shown that any such trivial zero is simple. We determine the exact degree of…