Related papers: On the Hitchin fibration for algebraic surfaces
We study underlying geometric structures for integral variational functionals, depending on submanifolds of a given manifold. Applications include (first order) variational functionals of Finsler and areal geometries with integrand the…
This is a review article on some applications of generalised parabolic structures to the study of torsion free sheaves and $L$-twisted Hitchin pairs on nodal curves. In particular, we survey on the relation between representations of the…
A Kauffman bracket on a surface is an invariant for framed links in the thickened surface, satisfying the Kauffman skein relation and multiplicative under superposition. This includes representations of the skein algebra of the surface. We…
We propose a geometric interpretation of the theory of elliptic endoscopy, due to Langlands and Kottwitz, in terms of the Hitchin fibration. As applications, we prove a global analog of a purity conjecture, due to Goresky, Kottwitz and…
We consider some planar triangular maps. These maps preserve certain fibration of the plane. We assume that there exists an invariant attracting fiber and we study the limit dynamics of those points in the basin of attraction of this…
The article is devoted to affine and wrap algebras over quaternions and octonions. Residues of functions of quaternion and octonion variables are studied. They are used for construction of such algebras. Their structure is investigated.
Mid-dimensional $(A,B,A)$ and $(B,B,B)$-branes in the moduli space of flat $G_{\mathbb C}$-connections appearing from finite group actions on compact Riemann surfaces are studied. The geometry and topology of these spaces is then described…
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…
We give a bound on embedding dimensions of geometric generic fibers in terms of the dimension of the base, for fibrations in positive characteristic. This generalizes the well-known fact that for fibrations over curves, the geometric…
This paper classifies Lagrangian fibrations over surfaces with compact total spaces up to fiberwise symplectomorphism identical on the base.
In this paper, we show some applications to algebraic cycles by using higher Abel-Jacobi maps which were defined in [the author: Motives and algebraic de Rham cohomology]. In particular, we prove that the Beilinson conjecture on algebraic…
We construct locally recoverable codes with hierarchy from surfaces in $\mathbb{A}^3$ admitting a fibration by curves of Artin-Schreier or Kummer type. We derive the parameters of our codes by leveraging the geometry and arithmetic of the…
The $\mathrm{PGL}_n(\mathbb{R})$-Hitchin component of a closed oriented surface is a preferred component of the character variety consisting of homomorphisms from the fundamental group of the surface to the projective linear group…
The base surface $B$ of a Lagrangian fibration $X\twoheadrightarrow B$ of a projective, irreducible symplectic fourfold $X$ is shown to be isomorphic to ${\mathbb P}^2$.
We prove the relation between the Hodge structure of the double cover of a nonsingular cubic surface branched along its Hessian and the Hodge structure of the triple cover of the ambient projective space branched along the cubic surface.…
We consider Hilbert algebras with a supplementary Fr\'echet topology and get various extensions of the algebraic structure by using duality techniques. In particular we obtain optimal multiplier-type involutive algebras, which in…
We compute the supports of the perverse cohomology sheaves of the Hitchin fibration for $GL_n$ over the locus of reduced spectral curves. In contrast to the case of meromorphic Higgs fields we find additional supports at the loci of…
By combining tools from different areas of mathematics, we obtain 3D visualizations of elliptic curves over different fields that faithfully capture the underlying algebra and geometry.
Algebraic surfaces in the complex projective space with a high number of A-type singularities have been presented in a recent paper. We extend the construction in order to obtain lower bounds for the maximal number of A singularities for…
In the present paper, we revisit the rigidity of hypersurfaces in Euclidean space. We highlight Darboux equation and give new proof of rigidity of hypersurfaces by energy method and maximal principle.