[en] We prove that any two irreducible cuspidal Hurwitz curves C₀ adn C₁ (or, more generally, two curves with A-type singularities) in the Hirzebruch surface F_N with the same homology classes and sets of singularities are regular homotopic. Moreover, they are symplectically regular homotopic if C₀ and C₁ are symplectic with respect to a compatible symplectic form

[en] A new irreducible component of the Gieseker–Maruyama moduli scheme M(3) of semistable coherent sheaves of rank 2 with Chern classes c₁ = 0, c₂ = 3, and c₃ = 0 on P³ such that its general point corresponds to a sheaf whose singular locus contains components of dimensions 0 and 1 is described. These sheaves are obtained by elementary transformations of stable reflexive sheaves of rank 2 with Chern classes c₁ = 0, c₂ = 2, and c₃ = 2 along the projective line. The constructed family of sheaves is the first example of an irreducible component of a Gieseker–Maruyama scheme whose general point corresponds to a sheaf with singularities of mixed dimension.

[en] We compute the degree complexity of a family of birational mappings of the plane with high order singularities

No abstract available

[en] We will study a monodromy preserving deformation with an irregular singular point and determine the τ-function of the monodromy preserving deformation by the elliptic θ-function moving the argument z and the period Ω

[en] We study the behaviour as /x/ → 0 of the solutions u=u(x) of the equation (1) Δu=V(/x/)u defined for 0
 On etudie le comportement en 0 des solutions u=u(x) de l'equation (1) Δu=V(/x/)u definies pour 0

No abstract available

[en] When relations are extrapolated beyond their premises of discovery, the operation sometimes results in an undefined object, i.e., one which cannot be identified within the given structure. The thesis is put forth that the occurrence of singularities is due to ''incompleteness'' in knowledge. An intuitive answer on how to deal with singularities (in, for instance, the real number system, space-time, quantum field theory) is presented first. Then a quasi-formalistic approach, e.g. non-standard models in higher-order languages and Lawvere's axiomatic formulation of categories, is set out. The independence of singularity with respect to other primitive notions of the Universe of knowledge is noted

[en] We propose a new expression for the generic additive discrete Painlevé equation associated with the affine Weyl group $E_8^{(1)}$. This expression makes the singularity analysis of the mapping perfectly straightforward and allows the implementation of the singularity confinement criterion in an extremely simple way. Using this new approach we derive new classes of discrete Painlevé equations related to $E_8^{(1)}$. (paper)

No abstract available