Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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EFFECTIVE RESULTS ON PICARD BUNDLES VIA M-REGULARITY
Get PDFIn this paper we study some properties, namely Global Generation and Strong Normal Presentation, of specific types of (twists of) Picard bundles over the Jacobian of a curve. Our main tool is the notion of M-regularity introduced by G. Pareschi and M.Popa.In this paper we study some properties, namely Global Generation andStrong Normal Presentation, of specific types of (twists of) Picard bundles over the Jacobian of a curve. Our main tool is the notion of M-regularity introduced by G. Pareschi and M.Popa
FOURIER-MUKAI TRANSFORMS OF LINE BUNDLES ON DERIVED EQUIVALENT ABELIAN VARIETIES
Get PDFWe study the Fourier-Mukai functor D(Y) → D(X) induced by the universal family on a fine moduli space Y for simple semihomogeneous vector bundles on an abelian variety X. The main result is that the Fourier-Mukai transform of a very negative line bundle on Y is ample if and only if the bundles parametrized by Y are nef.We study the Fourier-Mukai functor D(Y) → D(X) induced by theuniversal family on a fine moduli space Y for simple semihomogeneousvector bundles on an abelian variety X. The main result is that the Fourier-Mukai transform of a very negative line bundle on Y is ample if and only if the bundles parametrized by Y are nef
THE EQUATIONS OF SINGULAR LOCI OF AMPLE DIVISORS ON (SUBVARIETIES OF) ABELIAN VARIETIES
Get PDFIn this paper we consider ideal sheaves associated to the singular loci of a divisor in a linear system |L| of an ample line bundle on a complex abelian variety. We prove an effective result on their (continuous) global generation, after suitable twists by powers of L. Moreover we show that similar results hold for subvarieties of a complex abelian variety.In this paper we consider ideal sheaves associated to the singular lociof a divisor in a linear system |L| of an ample line bundle on a complexabelian variety. We prove an effective result on their (continuous) globalgeneration, after suitable twists by powers of L. Moreover we show thatsimilar results hold for subvarieties of a complex abelian variety
CLEAN RINGS OF SKEW HURWITZ SERIES
Get PDFIn this paper we study the transfer of some algebraic properties from the ring R to the ring of skew Hurwitz series T = (H R, σ ) where σ is an automorphism of R and vice versa. We show that T = (H R, σ ) is a clean (strongly clean) ring if and only if R is clean (strongly clean). Different properties of skew Hurwitz series are studied such as simplicity, primeness and semiprime.In this paper we study the transfer of some algebraic properties from the ring R to the ring of skew Hurwitz series T = (HR,σ) where σ is anautomorphism of R and vice versa. We show that T = (HR,σ) is a clean(strongly clean) ring if and only if R is clean (strongly clean). Different properties of skew Hurwitz series are studied such as simplicity, primeness and semiprime
EXISTENCE OF CONTINUOUS SOLUTIONS TO EVOLUTIONARY QUASI-VARIATIONAL INEQUALITIES WITH APPLICATIONS
Get PDFThe author presents dynamic elastic traffic equilibrium problems with data depending explicitly on time and studies under which assumptions the continuity of solutions with respect to the time can be ensured. In particular, regularity results for solutions to time-dependent quasi-variational inequalities associated to a general class of closed lower semicontinuous multifunctions will be showed. These results will be obtained making use of the property of the Mosco’s convergence. At last, it will be applied an example of the dynamic elastic traffic equilibrium problem.The author presents dynamic elastic traffic equilibrium problems withdata depending explicitly on time and studies under which assumptionsthe continuity of solutions with respect to the time can be ensured. In particular, regularity results for solutions to time-dependent quasi-variational inequalities associated to a general class of closed lower semicontinuous multifunctions will be showed. These results will be obtained making use of the property of the Mosco’s convergence. At last, it will be applied an example of the dynamic elastic traffic equilibrium problem
EXTENDING DIVISORS FROM COMPLETE INTERSECTION SURFACES
Get PDFThe aim of this paper is to extend a theorem of Griffiths, Harris and Hulek [4], [6] on the extendability of divisors of a smooth complete intersection surface in P^n to the case when the ambient space is a product of projective spaces or a Grassmannian. The proofs generalize the proof of the result of Griffiths-Harris-Hulek given by Ellingsrud-Gruson-Peskine-Strømme in [3].The aim of this paper is to extend a theorem of Griffiths, Harris and Hulek [4], [6] on the extendability of divisors of a smooth complete intersection surface in P^n to the case when the ambient space is a product of projective spaces or a Grassmannian. The proofs generalize the proof of the result of Griffiths-Harris-Hulek given by Ellingsrud-Gruson-Peskine-Strømme in [3]
A COMBINATORIAL GENERALIZATION OF THE DURFEE SQUARE
No full textThe Durfee square of a partition λ, D(λ), is defined as the largest square contained in the shape of λ.It was proved in [2] (cf. also [3]) that the size of D(λ), d(λ), was related to the perfection of a certain module M_λ , an algebro-geometric object (cf. also [1], [4], [5]). The goal of this note is to propose a generalization of the notion of Durfee square to the case of a pair (α, β) of partitions.The Durfee square of a partition λ, D(λ), is defined as the largestsquare contained in the shape of λ.It was proved in [2] (cf. also [3]) that the size of D(λ), d(λ),wasrelated to the perfection of a certain module Mλ, an algebro-geometricobject (cf. also [1], [4], [5]).The goal of this note is to propose a generalization of the notion ofDurfee square to the case of a pair (α, β) of partitions.More precisely, given two partitions α and β s.t. the last row of β isshorter then the first row of α, we define in Section 2, a partition D(α, β)(not necessarily a square), which we call “generalized Durfee partitionof α w.r.t. β”. D(α, β) is also related to algebro-geometric problems, asit is indicated for instance by the fact (proven in Section 3) that D(α, β)allows us to construct Lascoux’s rectification of α and β (cf. [8]).We conjecture that D(α, β) might encode important information onthe minimal free resolution of significant classes of modules (see, forinstance [10])
EVOLUTION PROBLEMS IN MATERIALS WITH FADING MEMORY
Get PDFEvolution problems in materials with memory are here considered.Thus, linear integro-differential equations with Volterra type kernel areinvestigated. Specifically, initial boundary value problems are studied;physical properties of the material under investigation are shown to induce the choice of a suitable function space, where solutions are looked for. Then, combination with the application of Fourier transforms, allows to prove existence and uniquenes of the solution. Indeed, the original evolution problem is related to an elliptic one: existence and uniqueness results are proved for the latter and, thus, for the original problem. Two different evolution initial boundary value problems with memory which arise, in turn, in the framework of linear heat conduction and of linear viscoelasticity are compared.Evolution problems in materials with memory are here considered.Thus, linear integro-differential equations with Volterra type kernel areinvestigated. Specifically, initial boundary value problems are studied;physical properties of the material under investigation are shown to induce the choice of a suitable function space, where solutions are looked for. Then, combination with the application of Fourier transforms, allows to prove existence and uniquenes of the solution. Indeed, the original evolution problem is related to an elliptic one: existence and uniqueness results are proved for the latter and, thus, for the original problem. Two different evolution initial boundary value problems with memory which arise, in turn, in the framework of linear heat conduction and of linear viscoelasticity are compared
Regularity of solutions of the Neumann problem for the Laplace equation
Get PDFLet u be a solution of the Neumann problem for the Laplace equation in G with the boundary condition g. It is shown that u ∈ L q (∂ G ) (equivalently, u ∈ Bq,21/q (G ) for 1 < q ≤ 2, u ∈ Lq 1/q (G ) for 2 ≤ q < ∞) if and only if the single layer potential corresponding to the boundary condition g is in L q (∂ G ). As a consequence we give a regularity result for some nonlinear boundary value problem
SOME REMARKS ON THE CANTOR PAIRING FUNCTION
Get PDFIn this paper, some results and generalizations about the Cantor pairingfunction are given. In particular, it is investigated a very compact expressionfor the n-degree generalized Cantor pairing function (g.C.p.f., for short), thatpermits to obtain n−tupling functions which have the characteristics to ben-degree polynomials with rational coefficients. A recursive formula for then-degree g.C.p.f. is also provided.In this paper, some results and generalizations about the Cantor pairingfunction are given. In particular, it is investigated a very compact expression for the n-degree generalized Cantor pairing function (g.C.p.f., for short), that permits to obtain n−tupling functions which have the characteristics to be n-degree polynomials with rational coefficients. A recursive formula for the n-degree g.C.p.f. is also provided