Wydział Matematyki i Informatyki | Faculty of Mathematics and Computer Science: Recent submissions
Now showing items 41-60 of 181
-
Gelfond-Mahler inequality for multipolynomial resultants
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)We give a bound of the height of a multipolynomial resultant in terms of polynomial degrees, the resultant of which applies. Additionally we give a Gelfond-Mahler type bound of the height of homogeneous divisors of a ... -
A family of hyperbolas associated to a triangle
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)In this note, we explore an apparently new one parameter family of conics associated to a triangle. Given a triangle we study ellipses whose one axis is parallel to one of sides of the triangle. The centers of these ellipses ... -
Rings and fields of constants of cyclic factorizable derivations
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)We present a survey of the research on rings of polynomial constants and fields of rational constants of cyclic factorizable derivations in polynomial rings over fields of characteristic zero. -
A few introductory remarks on line arrangements
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)Points and lines can be regarded as the simplest geometrical objects. Incidence relations between them have been studied since ancient times. Strangely enough our knowledge of this area of mathematics is still far from ... -
Extremal properties of line arrangements in the complex projective plane
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)In the present note we study some extreme properties of point-line configurations in the complex projective plane from a viewpoint of algebraic geometry. Using Hirzebruch-type inequalites we provide some new results on ... -
Finitely generated subrings of R[x]
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)In this article all rings and algebras are commutative with identity, and we denote by R[x] the ring of polynomials over a ring R in one variable x. We describe rings R such that all subalgebras of R[x] are finitely generated ... -
On the dual Hesse arrangement
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)In the present note we investigate to which extent the configuration of 9 lines intersecting in triples in 12 points is determined by these incidences. We show that up to a projective automorphism there is exactly one such ... -
Knots of irreducible curve singularities
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)In the article the relation between irreducible curve plane singularities and knots is described. In these terms the topological classification of such singularities is given. -
A note on divergence-free polynomial derivations in positive characteristic
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)In this paper we discuss an explicit form of divergence-free polynomial derivations in positive characteristic. It involves Jacobian derivations. -
A non-containment example on lines and a smooth curve of genus 10
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)The containment problem between symbolic and ordinary powers of homogeneous ideals has stimulated a lot of interesting research recently. In the most basic case of points in P2 and powers I(3) and I2, there is a number of ... -
Contact exponent and the Milnor number of plane curve singularities
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)We investigate properties of the contact exponent (in the sense of Hironaka [Hi]) of plane algebroid curve singularities over algebraically closed fields of arbitrary characteristic. We prove that the contact exponent is ... -
Preface
(Wydawnictwo Uniwersytetu Łódzkiego, 2019) -
When the medial axis meets the singularities
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)In this survey we present recent results in the study of the medial axes of sets definable in polynomially bounded o-minimal structures. We take the novel point of view of singularity theory. Indeed, it has been observed ... -
A note on the Łojasiewicz exponent of non-degenerate isolated hypersurface singularities
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)We prove that in order to find the value of the Łojasiewicz exponent ł(f) of a Kouchnirenko non-degenerate holomorphic function f : (Cn; 0) → (C; 0) with an isolated singular point at the origin, it is enough to find this ... -
Negative curves on special rational surfaces
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)We study negative curves on surfaces obtained by blowing up special configurations of points in P2. Our main results concern the following configurations: very general points on a cubic, 3–torsion points on an elliptic ... -
Andrzej Nowicki – Scientific biography
(Wydawnictwo Uniwersytetu Łódzkiego, 2019) -
Tadeusz Krasiński – Scientific biography
(Wydawnictwo Uniwersytetu Łódzkiego, 2019) -
Jacek Chadzynski – Scientific biography
(Wydawnictwo Uniwersytetu Łódzkiego, 2019) -
Wartości bifurkacyjne funkcji klasy C^\infty
(2019)Zbiorem wartości bifurkacyjnych funkcji gładkiej f:W->U nazywamy najmniejszy zbiór B zawarty w U taki, że funkcja f obcięta do zbioru f^{-1}(U\B) jest trywialną wiązką gładką. W pracy podajemy twierdzenia i metody pozwalające ... -
Skoki liczb Milnora deformacji liniowych osobliwości krzywych
(2019)Skokiem liczby Milnora osobliwości izolowanej f_0 nazywamy najmniejszą niezerową różnicę między liczbą Milnora osobliwości f_0 a liczbą Milnora jej deformacji f_s. Skok liczby Milnora dla osobliwości jednorodnych i ...