Rendiconti di Matematica e delle sue Applicazioni
ISSN 1120-7183 (print)
ISSN 2532-3350 (online)
Latest accepted papers, forthcoming into regular issues of the journal
Once a paper is accepted it goes immediately into production. It is a policy of the journal to publish papers online within four working weeks of acceptance.
Jon Eugster, Jonathan Pridham
An introduction to derived (algebraic) geometry
📥 Full Text (PDF format), published online 20 September 2023.
Abstract. Mostly aimed at an audience with backgrounds in geometry and homological algebra, these notes offer an introduction to derived geometry based on a lecture course given by the second author. The focus is on derived algebraic geometry, mainly in characteristic 0, but we also see the tweaks which extend most of the content to analytic and differential settings.
Federico Fallucca, Roberto Pignatelli
Smooth k-double covers of the plane of geometric genus 3
📥 Full Text (PDF format), published online 4 September 2023.
Abstract. In this work we classify all smooth surfaces with geometric genus equal to three and an action of a group G isomorphic to (Z/2)k such that the quotient is a plane. We find 11 families. We compute the canonical map of all of them, finding in particular a family of surfaces with canonical map of degree 16 that we could not find in the literature. We discuss the quotients by all subgroups of G finding several K3 surfaces with symplectic involutions. In particular we show that six families are families of triple K3 burgers in the sense of Laterveer.
Youssef Akdim, Mohammed El Ansari, Soumia Lalaoui Rhali
Solvability of some Stefan type problems with L1-data
📥 Full Text (PDF format), published online 18 July 2023.
Abstract. In this paper, we focus on some class of Stefan type problems. We prove the existence and uniqueness of renormalized solution in anisotropic Sobolev spaces with data belonging to L1-data, based on the properties of the renormalized solutions and the generalized monotonicity method in the functional spaces.
First integrals of nonlinear differential equations from nonlocal constants
📥 Full Text (PDF format), published online 3 July 2023.
Abstract. A new method to find first integrals of nonlinear differential equations in Jacobi-type form is presented. The basic idea of our approach is to use one-parameter perturbed motions to find well-conceived nonlocal constants that are conserved along solutions. By means of such nonlocal framework we derive a set of theorems that we apply to look for the first integrals of some relevant cases, where moreover a solution is obtained. Applications also include some equations of the Painlevé-Gambier classification
Arij Bouzelmate, Youssef Hajji, Hassane Hjiaj
Entropy solutions for some nonlinear p(x)-parabolic problems with degenerate coercivity
📥 Full Text (PDF format), published online 7 June 2023.
Abstract. Not available in HTML format