29 citations · 215 across the 37 of their papers we have counts for
38 papers
Ulrich sheaves, the arithmetic writhe and algebraic isotopies of space curves
Daniele Agostini, Mario Kummer
We establish a connection between the theory of Ulrich sheaves and -homotopy theory. For instance, we prove that the -degree of a morphism between proje…
Some thoughts and experiments on Bergman's compact amalgamation problem
Michael Joswig, Mario Kummer, Andreas Thom +1
We study the question whether copies of in can be amalgamated in a compact group. This is the simplest instance of a fundamental open problem in the theory o…
Bounding the signed count of real bitangents to plane quartics
Mario Kummer, Stephen McKean
Using methods from enriched enumerative geometry, Larson and Vogt gave a signed count of the number of real bitangents to real smooth plane quartics. This signed count depends on a…
A signed count of 2-torsion points on real abelian varieties
Mario Kummer
We prove that a natural signed count of the -torsion points on a real principally polarized abelian variety always equals to where is the dimension of . When…
Spectrahedral Shadows and Completely Positive Maps on Real Closed Fields
Manuel Bodirsky, Mario Kummer, Andreas Thom
In this article we develop new methods for exhibiting convex semialgebraic sets that are not spectrahedral shadows. We characterize when the set of nonnegative polynomials with a g…
Equivariant algebraic and semi-algebraic geometry of infinite affine space
Mario Kummer, Cordian Riener
We study -orbit closures of not necessarily closed points in the Zariski spectrum of the infinite polynomial ring $\mathbb{C}[x_{ij}:\, i\in\mathbb{N},\,j\in[…
Linear Principal Minor Polynomials: Hyperbolic Determinantal Inequalities and Spectral Containment
Grigoriy Blekherman, Mario Kummer, Raman Sanyal +2
A linear principal minor polynomial or lpm polynomial is a linear combination of principal minors of a symmetric matrix. By restricting to the diagonal, lpm polynomials are in bije…
Matroids on Eight Elements with the Half-plane Property and Related Concepts
Mario Kummer, Büşra Sert
We classify all matroids with at most 8 elements that have the half-plane property, and we provide a list of some matroids on 9 elements that have, and that do not have the half-pl…
Geography of pinched four-manifolds
Renato G. Bettiol, Mario Kummer, Ricardo A. E. Mendes
We prove several new restrictions on the Euler characteristic and signature of oriented 4-manifolds with (positively or negatively) pinched sectional curvature. In particular, we s…
Iso Edge Domains
Mathieu Dutour Sikirić, Mario Kummer
Iso-edge domains are a variant of the iso-Delaunay decomposition introduced by Voronoi. They were introduced by Baranovskii & Ryshkov in order to solve the covering problem in dime…
Real-fibered morphisms of del Pezzo surfaces and conic bundles
Mario Kummer, Cédric Le Texier, Matilde Manzaroli
It goes back to Ahlfors that a real algebraic curve admits a real-fibered morphism to the projective line if and only if the real part of the curve disconnects its complex part. In…
Nodes on quintic spectrahedra
Taylor Brysiewicz, Khazhgali Kozhasov, Mario Kummer
We classify transversal quintic spectrahedra by the location of 20 nodes on the respective real determinantal surface of degree 5. We identify 65 classes of such surfaces and find…
A generalization of the space of complete quadrics
Abeer Al Ahmadieh, Mario Kummer, Miruna-Stefana Sorea
To any homogeneous polynomial we naturally associate a variety which maps birationally onto the graph of the gradient map and which agrees with the space…
Spectral linear matrix inequalities
Mario Kummer
We prove, under a certain representation theoretic assumption, that the set of real symmetric matrices, whose eigenvalues satisfy a linear matrix inequality, is itself a spectrahed…
Positive Ulrich Sheaves
Christoph Hanselka, Mario Kummer
We provide a criterion for a coherent sheaf to be an Ulrich sheaf in terms of a certain bilinear form on its global sections. When working over the real numbers we call it a positi…
Rational functions with only real periodic points
Khazhgali Kozhasov, Mario Kummer
We study self-morphisms of smooth real projective algebraic curves that have only real periodic points. In the case of the projective line we provide a convenient characterization…
Hyperbolic Secant Varieties of M-Curves
Mario Kummer, Rainer Sinn
We relate the geometry of curves to the notion of hyperbolicity in real algebraic geometry. A hyperbolic variety is a real algebraic variety that (in particular) admits a real fibe…
On Huisman's conjectures about unramified real curves
Mario Kummer, Dimitri Manevich
Let be an unramified real curve with . If is odd, Huisman conjectures that is an -curve and that every br…
Convex Algebraic Geometry of Curvature Operators
Renato G. Bettiol, Mario Kummer, Ricardo A. E. Mendes
We study the structure of the set of algebraic curvature operators satisfying a sectional curvature bound under the light of the emerging field of Convex Algebraic Geometry. More p…
The multidimensional truncated Moment Problem: Carathéodory Numbers from Hilbert Functions
Philipp J. di Dio, Mario Kummer
In this paper we improve the bounds for the Carathéodory number, especially on algebraic varieties and with small gaps (not all monomials are present). We provide explicit lower an…
Spectrahedral representations of plane hyperbolic curves
Mario Kummer, Simone Naldi, Daniel Plaumann
We describe a new method for constructing a spectrahedral representation of the hyperbolicity region of a hyperbolic curve in the real projective plane. As a consequence, we show t…
Generalized eigenvalue methods for Gaussian quadrature rules
Grigoriy Blekherman, Mario Kummer, Cordian Riener +2
A quadrature rule of a measure on the real line represents a convex combination of finitely many evaluations at points, called nodes, that agrees with integration against f…
Totally real theta characteristics
Mario Kummer
A totally real theta characteristic of a real curve is a theta characteristic which is linearly equivalent to a sum of only real points. These are closely related to the facets of…
Schottky Algorithms: Classical meets Tropical
Lynn Chua, Mario Kummer, Bernd Sturmfels
We present a new perspective on the Schottky problem that links numerical computing with tropical geometry. The task is to decide whether a symmetric matrix defines a Jacobian, and…