Related papers: On fibrations approaching the Arakelov equality

Faltings conjectured that under the p-adic Simpson correspondence, finite dimensional p-adic representations of the geometric \'etale fundamental group of a smooth proper p-adic curve X are equivalent to semi-stable Higgs bundles of degree…

We study torsion-free, rank 2 Higgs sheaves on genus one fibered surfaces, (semi)stable with respect to suitable polarizations in the sense of Friedman and O'Grady. We prove that slope-semistability of a Higgs sheaf on the surface implies…

Let $G$ be a finite abelian group of order $n$, and for each $a\in G$ and integer $1\le h\le n$ let $\mathcal{F}_a(h)$ denote the family of all $h$-element subsets of $G$ whose sum is $a$. A problem posed by Katona and Makar-Limanov is to…

We prove that the normal bundle of a general Brill-Noether curve of genus $g \geq 1$ and degree $d$ in $\mathbb{P}^r$ is semistable if $g=1$ or $g\geq \left \lceil \frac{5r}{2}\right\rceil r(r-1)$, or $d$ is larger than an explicit function…

We introduce $\mathfrak{f}$-stability, a modification of fibration stability of Dervan-Sektnan [12], and show that $\mathfrak{f}$-semistable fibrations have only semi log canonical singularities. Moreover, $\mathfrak{f}$-stability puts…

For each g > 2 and h > 1, we explicitly construct (1) fiber sum indecomposable relatively minimal genus g Lefschetz fibrations over genus h surfaces whose monodromies lie in the Torelli group, (2) fiber sum indecomposable genus g surface…

We establish positive mass type theorems for asymptotically locally flat (ALF) manifolds, which have asymptotic ends modeled on circle bundles over a Euclidean base with fibers of constant length. In particular for dimensions $n\leq 7$, the…

Let $f:\, S \to B$ be a locally non-trivial relatively minimal fibration of hyperelliptic curves of genus $g\geq 2$ with relative irregularity $q_f$. We show a sharp lower bound on the slope $\lambda_f$ of $f$. As a consequence, we prove a…

Let $L$ be a (semi)-positive line bundle over a Kahler manifold, $X$, fibered over a complex manifold $Y$. Assuming the fibers are compact and non-singular we prove that the hermitian vector bundle $E$ over $Y$ whose fibers over points $y$…

Let $f:E\longrightarrow O$ be a Hurewicz fibration with a fiber space $F_{r_{o}}$ and a lifting function $L_{f}$. The \emph{$Lf-$function} $\Theta_{L_{f}}$ of $f$ is defined by the restriction map of $L_{f}$ on the space…

In this paper we show that a Brownian Gibbsian line ensemble whose top curve approximates a parabola must be given by the parabolic Airy line ensemble. More specifically, we prove that if $\boldsymbol{\mathcal{L}} = (\mathcal{L}_1,…

Let $\pi\cln X\to \Delta^m$ be a proper smooth K\"ahler morphism from a complex manifold $X$ to the unit polydisc $\Delta^m$. Suppose the fibers over the complement of a proper analytic subset are biholomorphic to a fixed projective…

In this paper we prove a Sobolev and a Morrey type inequality involving the mean curvature and the tangential gradient with respect to the level sets of the function that appears in the inequalities. Then, as an application, we establish…

If one thinks of a Riemannian metric, $g_1$, analogously as the gradient of the corresponding distance function, $d_1$, with respect to a background Riemannian metric, $g_0$, then a natural question arises as to whether a corresponding…

Let $S$ be a minimal irregular surface of general type, whose Albanese map induces a fibration $f:\,S \to C$ of genus $g$.We prove a linear upper bound on the genus $g$ if $K_S^2\leq 4\chi(\mathcal{O}_S)$. Examples are constructed showing…

In this paper we study the arithmetic invariants of Euclidean lattice in the context of Arakelov geometry. We regard a Euclidean lattice as a hermitian vector bundle $\bar E$ on ${\rm Spec}(\mathbb{Z})$ and consider two typical arithmetic…

Let C be a smooth projective curve with genus g>1 and Clifford index c(C) and let L be a line bundle on C generated by its global sections. The morphism i:C -->P(H^0(L))=P is well-defined and i*T is the restriction to C of the tangent…

We describe the Harder--Narasimhan filtration of the Hodge bundle for Teichm\"uller curves in the non-varying strata of quadratic differentials appearing in [CM2]. Moreover, we show that the Hodge bundle on the non-varying strata away from…

Given a holomorphic vector bundle $E$ on the twistor space $\mathrm{Tw}(M)$ of a simple hyperk\"ahler manifold $M$, we view it as a family of bundles $\left\{E_I\right\}$ on the fibres $\pi^{-1}(I)$ of the twistor projection $\pi :…

In this paper we compute the asymptotics of the metric on the line bundle over the moduli space of curves that arises when attempting to compute the archimedean height of the algebraic cycle $C-C^-$ in the jacobian of a smooth projective…