相关论文: On Cremona Transformations of P^3 with all possibl…

We study the existence of a decomposition of the diagonal for bidegree hypersurfaces in a product of projective spaces. Using a cycle theoretic degeneration technique due to Lange, Pavic and Schreieder, we develop an inductive procedure…

We classify all monomial planar Cremona maps by multidegree using recent methods developed by Aluffi. Following the main result, we prove several more properties of the set of these maps, and also extend the results to the more general…

In this paper we deal with linear systems of P^3 through fat points. We consider the behavior of these systems under a cubo-cubic Cremona transformation that allows us to produce a class of special systems which we conjecture to be the only…

The $\kappa$-deformation of the D-dimensional Poincar\'e algebra $(D\geq 2)$ with any signature is given. Further the quadratic Poisson brackets, determined by the classical $r$-matrix are calculated, and the quantum Poincar\'e group "with…

Let d_3 >= p_2 > p_1 >= 3 be integers such that p_1,p_2 are prime numbers. In this paper we show that the sequence (p_1,p_2,d_3) is the multidegree of some tame automorphisms of C^3 if and only if d_3 is in p_1*N+p_2*N, i.e. if and only if…

A homogeneous polynomial of degree $d$ in $n+1$ variables is identifiable if it admits a unique additive decomposition in powers of linear forms. Identifiability is expected to be very rare. In this paper we conclude a work started more…

In this paper we compute the number of n degree representations of a group of order p^3 for p an odd prime and the dimensions of corresponding spaces of invariant bilinear forms over an algebraically closed field F. We explicitly discuss…

Fourdimensional bicovariant differential calculus on quantum E(2) group is constructed.

Point transformations for the ordinary differential equations of the form $y''=P(x,y)+3 Q(x,y) y'+3 R(x,y) (y')^2+S(x,y) (y')^3$ are considered. Some classical results are resumed. Solution for the equivalence problem for the equations of…

A famous result of B. Crauder and S. Katz (1989) concerns the classification of special Cremona transformations whose base locus has dimension at most two. Furthermore, they also proved that a special Cremona transformation with base locus…

We deal with the following question of Dolgachev : is the Cremona group generated by involutions ? Answer is yes in dimension $2$ (Cerveau-Deserti). We give an upper bound of the minimal number $\mathfrak{n}_\varphi$ of involutions we need…

We study the minimal bigraded free resolution of an ideal with three generators of the same bidegree, contained in the bihomogeneous maximal ideal $ \langle s,t\rangle \cap \langle u,v \rangle$ of the bigraded ring K[s,t;u,v]. Our analysis…

We prove the weight part of Serre's conjecture in generic situations for forms of $U(3)$ which are compact at infinity and split at places dividing $p$ as conjectured by Herzig. We also prove automorphy lifting theorems in dimension three.…

In this note we observe that the Cremona transformation in Oguiso's example of Cremona isomorphic but not projectively equivalent quartic K3 surfaces in three-dimensional projective space is the classical cubo-cubic transformation.

For any $n\geq 3$, we prove that there exist equivalences between these apparently unrelated objects: irreducible $n$-dimensional non degenerate projective varieties $X\subset \mathbb P^{2n+1}$ different from rational normal scrolls and…

We introduce invariants for compact $C^1$-orientable surfaces (with boundary) in $\mathbb{R}^3$ up to rigid transformations. Our invariants are certain degree four polynomials in the moments of the delta function of the surface. We give an…

This paper is concerned with suitable generalizations of a plane de Jonqui\`eres map to higher dimensional space $\mathbb{P}^n$ with $n\geq 3$. For each given point of $\mathbb{P}^n$ there is a subgroup of the entire Cremona group of…

We study families of elliptic curves of degree n+1 in $P^n$ containing a fixed set of m points. In the case m = n+3 we show that this family is birationally isomorphic to a smooth complete intersection of n-2 diagonal quadrics in $P^{n+2}$.…

Let k be an algebraically closed field. We show that the Cremona group of all birational transformations of the projective plane P^2 over k is not a simple group. The strategy makes use of hyperbolic geometry, geometric group theory, and…

We discuss the concept of Cremona contractible plane curves, with an historical account on the development of this subject. We then classify Cremona contractible unions of d > 11 lines in the plane.