Related papers: Objectivity and Rigor in Classical Italian Algebra…
This is a detailed write-up of Koll\'ar's course at the EMS summer school in Algebraic Geometry in Eger, Hungary, August 1996. The topics include definitions and examples of rational and unirational varieties, with special attention to…
The works of R. Descartes, I. M. Gelfand and A. Grothendieck have convinced us that commutative rings should be thought of as rings of functions on some appropriate (commutative) spaces. If we try to push this notion forward we reach the…
Divided into three parts, the first marks out enormous geometric issues with the notion of quasi-freenss of an algebra and seeks to replace this notion of formal smoothness with an approximation by means of a minimal unital commutative…
The relationship between convex geometry and algebraic geometry has deep historical roots, tracing back to classical works in enumerative geometry. In this paper, we continue this theme by studying two interconnected problems regarding…
Geometric algebra was initiated by W.K. Clifford over 130 years ago. It unifies all branches of physics, and has found rich applications in robotics, signal processing, ray tracing, virtual reality, computer vision, vector field processing,…
In 2005, building on his own recent work and that of F. Zanello, A. Iarrobino discovered some constructions that, he conjectured, would yield level algebras with non-unimodal Hilbert functions. This thesis provides proofs of non-unimodality…
Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to…
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…
We verify that elliptic K3 surfaces and algebraic groups have many rational points over function fields, i.e., they are geometrically special in the sense of Javanpeykar-Rousseau. We also show that under additional assumptions, this…
Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…
The division of compact Riemann surfaces into 3 cases K_C<0, g=0, or K_C=0, g=1, or K_C>0, g>=2 is well known, and corresponds to the familiar trichotomy of spherical, Euclidean and hyperbolic non-Euclidean plane geometry. Classification…
The concept of viewing graph solvability has gained significant interest in the context of structure-from-motion. A viewing graph is a mathematical structure where nodes are associated to cameras and edges represent the epipolar geometry…
The development of computational techniques in the last decade has made possible to attack some classical problems of algebraic geometry. In this survey, we briefly describe some open problems related to algebraic curves which can be…
The paper suggests a short survey of integration algorithms which evolved since 1982. These theorems and algorithms form discrete versions of the calculus theorems.
For a smooth minimal surface of general type $S$ with $Albdim(S) = 2$, Severi inequality says that $K_S^2 \geq 4\chi(S)$, which was proved by Pardini. It is expected that when the equality is attained, $S$ is birational to a double cover…
We prove the so-called Severi inequality, stating that the invariants of a minimal smooth complex projective surface of maximal Albanese dimension satisfy: K^2_S >= 4\chi(S).
In an impressive series of papers, Krivine showed at the edge of the last decade how classical realizability provides a surprising technique to build models for classical theories. In particular, he proved that classical realizability…
Research evaluations and comparison of the assessments of academic institutions (scientific areas, departments, universities etc.) are among the major issues in recent years in higher education systems. One method, followed by some national…
Based on the distinction between the covariant and contravariant metric tensor components in the framework of the affine geometry approach and the s.c. "gravitational theories with covariant and contravariant connection and metrics", it is…
The traditional study of plane and space algebraic curves by looking at their tangent vectors, curvatures and torsions provides geometric, but unfortunately not sufficient information about individual curves in order to be able to…