Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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On the principally polarized abelian varieties with m-minimal curves
Full text linkIn this paper, we study principally polarized abelian varieties X of dimension g with a curve C such that the class of C is m times theminimal class. Welters introduced the formalism of complementarypairs to handle this problem in the case m = 2. We generalize the results of Welters and construct families of principally polarized abelian varieties for any m and compute the dimension of the locus of these abelian varieties
Isogenies of Prym varieties
Full text linkWe prove an extension of the Babbage-Enriques-Petri theorem for semi-canonical curves. We apply this to show that the Prym variety of a generic element of a codimension subvariety of \kr_g is not isogenous to another distinct Prym variety, under some mild assumption on
Qualitative and quantitative uncertainty Principles for the generalized Fourier transform associated with the Riemann-Liouville operator
Full text linkThe aim of this paper is to establish anextension of qualitative and quantitativeuncertainty principles forthe Fourier transform connected with the Riemann-Liouville operator
Dunkl-semiclassical orthogonal polynomials. The symmetric case.
Full text linkIn this paper, we introduce a new class of symmetric orthogonal polynomials that generalizes the class of Dunkl-classical ones. As applications, we give some new characterizations of the symmetric semiclassical orthogonal polynomials
Curvilinear schemes and maximum rank of forms
Full text linkWe define the \emph{curvilinear rank} of a degree form in variables as the minimum length of a curvilinear scheme, contained in the -th Veronese embedding of , whose span contains the projective class of . Then, we give a bound for rank of any homogenous polynomial, in dependance on its curvilinear rank
Non uniform projections of surfaces in
Full text linkConsider the projection of a smooth irreducible surface in from a point.The uniform position principle implies that the monodromy group of such a projection from a general point in is the whole symmetric group. We will call such points uniform. Inspired by a result of Pirola and Schlesinger for the case of curves, we proved that the locus of non-uniform points of is at most finite
q-Weierstrass transform associated with the q-Fourier Bessel operator
Full text linkThis work deals with the reproducing kernels in Hilbert spaces. Namely, we study the Weierstrass transform in quantum calculus related to the Fourier Bessel transform and we give the appropriate best approximations
R-parts and modules derived from strongly U-regular relations on hypermodules
Full text linkThis paper concerns a new relationship between hypermodules and modules. We generalize the notion of complete parts and -parts by the notion of -parts on hypermodulesand then -closures of hypermodules as a generalization of -closures are defined. In addition,we give the notion of a strongly -regular relation on hypermodules and investigate some properties of it
Low Codimension Strata of the Singular Locus of Moduli of Level Curves
Full text linkWe further analyse the moduli space of stable curves with level structure provided by Chiodo and Farkas in [2]. Their result builds upon Harris and Mumford analysis of the locus of singularities of the moduli space of curves and shows in particular that for levels 2, 3, 4, and 6 the locus of noncanonical singularities is completely analogous to the locus described by Harris and Mumford, it has codimension 2 and arises from the involution of elliptic tails carrying a trivial level structure. For the remaining levels (5, 7, and beyond), the picture also involves components of higher codimension.We show that there exists a component of codimension 3 for levels ℓ = 5 and ℓ > 7 with the only exception of level 12. We also show that there exists a component of codimension 4 for ℓ = 12
Existence of periodic solutions for a second-order nonlinear neutral differential equation by the Krasnoselskii\u27s fixed point technique
Full text linkThe objective of this work is the application of Krasnoselskii\u27s fixed point technique to prove the existence of periodic solutions of the second-order nonlinear neutral differential equation ((d²)/(dt²))x(t)+p(t)(d/(dt))x(t)+q(t)x(t)=((d²)/(dt²))g(t,x(t-τ(t)))+f(t,x(t),x(t-τ(t))).The idea of this technique is based on the inverting of the considered equation into an integral equation whose solution is recourse to Krasnoselskii\u27s fixed point theorem. In addition, by application of the Banach principle on the inverted integral equation and under certain specified constraints we proved the uniqueness of the periodic solution