Related papers: J-embeddable reducible surfaces (enlarged version)
A (d+1)-dimensional dispersionless PDE is said to be integrable if its n-component hydrodynamic reductions are locally parametrized by (d-1)n arbitrary functions of one variable. Given a PDE which does not pass the integrability test, the…
We study threefolds X in a projective space having as hyperplane section a smooth surface with an elliptic fibration. We first give a general theorem about the possible embeddings of such surfaces with Picard number two. More precise…
By a result of Orlov there always exists an embedding of the derived category of a finite-dimensional algebra of finite global dimension into the derived category of a high-dimensional smooth projective variety. In this article we give some…
Let K be a CM-field, i.e., a totally complex quadratic extension of a totally real field F. Let X be a g-dimensional abelian variety admitting an algebra embedding of F into the rational endomorphisms End_Q(X) of X. Let A be the product of…
We initiate a study of varieties of minimal degree in weighted projective spaces. We call a weighted projective space $\mathbf{P}(w_0,\dots,w_n)$ divisible if $w_i \mid w_{i+1}$ for all $i$. We provide sharp bounds for when a non-degenerate…
In this paper we study maps (curved flats) into symmetric spaces which are tangent at each point to a flat of the symmetric space. Important examples of such maps arise from isometric immersions of space forms into space forms via their…
We study permutation-invariant embeddings of $d$-dimensional point sets, which are defined by sorting $D$ independent one-dimensional projections of the input. Such embeddings arise in graph deep learning where outputs should be invariant…
We prove the following result: Let B be a smooth, irreducible, quasi-projective variety over the complex numbers and assume that B has a projective compactification \bar{B} such that \bar{B} - B is of codimension at least two in \bar{B}.…
Generalized Weierstrass representations for generic surfaces conformally immersed into four-dimensional Euclidean and pseudo-Euclidean spaces of different signatures are presented. Integrable deformations of surfaces in these spaces…
This paper aims at the following results: \begin{enumerate} \item The class of all $*$-regular rings forms a variety. \item A subdirectly irreducible $*$-regular ring $R$ is faithfully representable (i.e. isomorphic to a subring of an…
A local description of the non-flat infinitesimally bendable Euclidean hypersurfaces was recently given by Dajczer and Vlachos \cite{DaVl}. From their classification, it follows that there is an abundance of infinitesimally bendable…
A projective structure is Weyl metrizable if it has a representative that preserves a conformal structure. We interpret Weyl metrizability of 3-dimensional projective structures as certain 5-dimensional nondegenerate CR submanifolds in a…
We study three different kinds of embeddings of tree patterns: weakly-injective, ancestor-preserving, and lca-preserving. While each of them is often referred to as injective embedding, they form a proper hierarchy and their computational…
A set of multi-homogeneous equations for the Jacobian of a genus two curve is given. The approach used is to write down affine equations for the Jacobian minus various tranlations of the Theta-divisor by [2]-division points, and then to…
We prove that the isometric embedding of any metric of differentiability class C1 in E3 exists. We use simplified notation for the given metric, namely geodesic parameters, and level parameters for the embedded surface in E3. Central to our…
We present a complete classification of complex projective surfaces $X$ with nontrivial self-maps (i.e. surjective morphisms $f:X\rightarrow X$ which are not isomorphisms) of any given degree. The starting point of our classification are…
The aim of this paper is to investigate the differential geometry of immersed surfaces in three-dimensional normed spaces from the viewpoint of affine differential geometry. We endow the surface with a useful Riemannian metric which is…
In this paper we prove a conjecture of Bryant, Griffiths, and Yang concerning the characteristic variety for the determined isometric embedding system. In particular, we show that the characteristic variety is not smooth for any dimension…
We introduce a class of volume-contracting surface diffeomorphisms whose dynamics is intermediate between one-dimensional dynamics and general surface dynamics. For that type of systems one can associate to the dynamics a reduced…
For any smooth complex projective surface $S$, we construct semistable refined Vafa-Witten invariants of $S$ which prove the main conjecture of arXiv:1810.00078. This is done by extending part of Joyce's universal wall-crossing formalism to…