Related papers: Quadro-quadric cremona transformations in low dime…
In the present work we describe 3-dimensional complex SL_2-varieties where the generic SL_2-orbit is a surface. We apply this result to classify the minimal 3-dimensional projective varieties with Picard-number 1 where a semisimple group…
In this paper, we present some basic properties concerning the quasi-derivation algebra $QDer(\mathcal{A})$ and the quasi-centroid algebra $QC(\mathcal{A})$ of associative algebra $\mathcal{A}$. Furthermore, using the result on…
In this lecture I discuss jet-shape distributions and describe how from jet evolution one may design Monte Carlo simulations which are used in the analysis of short distance distributions in $\ee$-annihilation, lepton-hadron and…
In this note we elaborate on the reduction of four dimensional Seiberg duality with adjoint matter to three dimensions. We use the exact formulation of the superconformal index and of the partition function as instruments to test this…
We study low order terms of Emerton's spectral sequence for simply connected, simple groups. As a result, for real rank 1 groups, we show that Emerton's method for constructing eigenvarieties is successful in cohomological dimension 1. For…
Connecting curves have been shown to organize the rotational structure of strange attractors in three-dimensional dynamical systems. We extend the description of connecting curves and their properties to higher dimensions within the special…
We construct Cremona transformations of P^3 with bidegrees (d,e), where d<e^2+1, e< d^2+1 and d,e> 0.
It is shown that certain transformations on quiver-dimension vector pairs induce isomorphisms on the corresponding moduli spaces of quiver representations and map a stable dimension vector to a stable dimension vector. This result combined…
Recent developments in the evaluation of vector-meson spectral functions in hot and dense matter are discussed with emphasis on connections to the chiral phase transition in QCD. Model independent approaches including chiral low-density…
The works of Brunella and Santos have singled out three special singular holomorphic foliations on projective surfaces having invariant rational nodal curves of positive self-intersection. These foliations can be described as quotients of…
We study deformations of complex projective varieties that are homotopically or homologically trivial. We formulate several conjectures and give some examples and partial answers.
In the previous paper [E-print alg-geom/9507004] we classified the rational cuspidal plane curves C with a cusp of multiplicity deg C - 2. In particular, we showed that any such curve can be transformed into a line by Cremona…
We study embeddings of symmetric groups to the space Cremona group.
Minimal surfaces play a fundamental role in differential geometry, with applications spanning physics, material science, and geometric design. In this paper, we explore a novel quaternionic representation of minimal surfaces, drawing an…
This paper is an adaptation of a chapter from an upcoming monograph on noncommutative geometry and quantum groups. We present examples of non compact quantum groups which are deformations of low dimensional Lie groups. The paper is of…
We study, theoretically and experimentally, a 1-parameter family of transformations and their limiting vector field on the space of plane polygons. These transformations are discrete analogs of completely integrable transformation on closed…
We study finite-dimensional commutative algebras, which satisfy the Jacobi identity. Such algebras are Jordan algebras. We describe some of their properties and give a classification in dimensions $n<7$ over algebraically closed fields of…
In this note we begin a systematic study of compact conformal manifolds of SCFTs in four dimensions (our notion of compactness is with respect to the topology induced by the Zamolodchikov metric). Supersymmetry guarantees that such…
The Cremona group of rank n over a field k is the group of birational automorphisms of the n-dimensional projective space over the field k. We study the minimal dimension such that all finite subgroups of the Cremona group have a faithful…
In this paper we introduce a new invariant for a non-degenerate evolution algebra, which consists of an ordered sequence of evolution algebras of lower dimension, belonging all of them to a specific family. We use this invariant to propose…