Related papers: Algebraic hypersurfaces
The article surveys published and not yet published results about moduli spaces of algebraic surfaces.
In this position paper, we promote the study of function spaces parameterized by machine learning models through the lens of algebraic geometry. To this end, we focus on algebraic models, such as neural networks with polynomial activations,…
We develop basic notions and methods of algebraic geometry over the algebraic objects called hyperrings. Roughly speaking, hyperrings generalize rings in such a way that an addition is `multi-valued'. This paper largely consisits of two…
We investigate proper biharmonic hypersurfaces with at most three distinct principal curvatures in space forms. We obtain the full classification of proper biharmonic hypersurfaces in 4-dimensional space forms.
Mostly aimed at an audience with backgrounds in geometry and homological algebra, these notes offer an introduction to derived geometry based on a lecture course given by the second author. The focus is on derived algebraic geometry, mainly…
A survey on recent developments in (algebraic) integral geometry is given. The main focus lies on algebraic structures on the space of translation invariant valuations and applications in integral geometry.
In this paper, we study hypersurfaces in $\mathbb{H}^2\times\mathbb{H}^2$. We first classify the hypersurfaces with constant principal curvatures and constant product angle function. Then, we classify homogeneous hypersurfaces and…
We survey recent developments on rationality problems for algebraic varieties, with a particular emphasis on cycle-theoretic and combinatorial methods and their applications to hypersurfaces.
This text is a short but comprehensive introduction to the basics of supergeometry and includes some of the recent advances in colored supergeometry. We do not aim for a standard text that states results and proves them more or less…
Some basic notions of classical algebraic geometry can be defined in arbitrary varieties of algebras $\Theta.$ For every algebra $H$ in $\Theta$ one can consider algebraic geometry in $\Theta$ over $ H.$ Correspondingly, algebras in…
This paper first gives a brief overview over some interesting descriptions of conic sections, showing formulations in the three geometric algebras of Euclidean spaces, projective spaces, and the conformal model of Euclidean space. Second…
A description of group automorphisms of all two-dimensional algebras, considered up to isomorphism, over any basic field is provided.
The paper is focused on the four-dimensional visualization of hypersurfaces represented by implicit equations without their parametrization. We describe a general method to find shadow boundaries in an arbitrary dimension and apply it in a…
The set of matrix tuples with invariant subspaces whose dimensions sum up to the dimension of the space, but which do not span the whole space form an algebraic hypersurface. We found the equation of this hypersurface. This generalizes…
The topics of Convexity and Concavity and Envelopes are central in Complex Analysis and extensively investigated. The aim of this paper is to find a possible counterpart in Algebraic Geometry. The article presents preliminary results on…
We show that the definition of an algebraic basis for a vector space allows the construction of an isomorphism with the one here called Algebraic Vector Space. Although the concept does not bring anything new, we mention some of the…
We give an elementary introduction to hyperk\"ahler manifolds, survey some of their interesting properties and some open problems.
In this paper, we study the computation of curvatures at the singular points of algebraic curves and surfaces. The idea is to convert the problem to compute the curvatures of the corresponding regular parametric curves and surfaces, which…
In this survey article, we present interactions between algebraic geometry and computer vision, which have recently come under the header of algebraic vision. The subject has given new insights in multiple view geometry and its application…
In this paper, we study the persistent homology of the offset filtration of algebraic varieties. We prove the algebraicity of two quantities central to the computation of persistent homology. Moreover, we connect persistent homology and…