- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 11:09:49
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https://www.ems-ph.org/meta/jmeta-stream.php?jrn=RSMUP&vol=126&update_since=2024-03-29
Rendiconti del Seminario Matematico della Università di Padova
Rend. Sem. Mat. Univ. Padova
RSMUP
0041-8994
2240-2926
General
10.4171/RSMUP
http://www.ems-ph.org/doi/10.4171/RSMUP
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126
2011
0
A Note on Minimal Galois Embeddings of Abelian Surfaces
Hisao
Yoshihara
Niigata University, NIIGATA, JAPAN
We show that the least number $N$ such that an abelian surface has a Galois embedding in $\mathbb{P}^N$ is seven and then we give examples of such surfaces.
General
1
9
10.4171/RSMUP/126-1
http://www.ems-ph.org/doi/10.4171/RSMUP/126-1
Rational Components of Hilbert Schemes
Paolo
Lella
Università degli Studi di Torino, TORINO, ITALY
Margherita
Roggero
Università degli Studi di Torino, TORINO, ITALY
The Groebner stratum of a monomial ideal $\mathfrak{j}$ is an affine variety that parameterizes the family of all ideals having $\mathfrak{j}$ as initial ideal (with respect to a fixed term ordering). The Groebner strata can be equipped in a natural way with a structure of homogeneous variety and are in a close connection with Hilbert schemes of subschemes in the projective space $\mathbf{P}^n$. Using properties of the Groebner strata we prove some sufficient conditions for the rationality of components of ${\mathcal{H}\text{ilb}_{p(z)}^n}$. We show for instance that all the smooth, irreducible components in ${\mathcal{H}\text{ilb}_{p(z)}^n}$ (or in its support) and the Reeves and Stillman component $H_{RS}$ are rational. We also obtain sufficient conditions for isomorphisms between strata corresponding to pairs of ideals defining a same subscheme, that can strongly improve an explicit computation of their equations.
General
11
45
10.4171/RSMUP/126-2
http://www.ems-ph.org/doi/10.4171/RSMUP/126-2
Quadratic Integral Solutions to Double Pell Equations
Francesco
Veneziano
Scuola Normale Superiore, PISA, ITALY
We study the quadratic integral points--that is, ($S$-)integral points defined over any extension of degree two of the base field--on a curve defined in $\mathbb{P}_3$ by a system of two Pell equations. Such points belong to three families explicitly described, or belong to a finite set whose cardinality may be explicitly bounded in terms of the base field, the equations defining the curve and the set $S$. We exploit the peculiar geometry of the curve to adapt the proof of a theorem of Vojta, which in this case does not apply.
General
47
61
10.4171/RSMUP/126-3
http://www.ems-ph.org/doi/10.4171/RSMUP/126-3
Root Separation for Reducible Monic Quartics
Andrej
Dujella
University of Zagreb, ZAGREB, CROATIA
Tomislav
Pejkovič
University of Zagreb, ZAGREB, CROATIA
We study root separation for reducible monic integer polynomials of degree four. If $\text{H}(P)$ is the height and $\text{sep}(P)$ the minimal distance between two distinct roots of a separable integer polynomial $P(x)$, and $\text{sep}(P)=\text{H}(P)^{-e(P)}$, we show that $\limsup e(P)=2$, where limsup is taken over all reducible monic integer polynomials $P(x)$ of degree $4$.
General
63
72
10.4171/RSMUP/126-4
http://www.ems-ph.org/doi/10.4171/RSMUP/126-4
Finite Groups with Weakly $s$-Semipermutable Subgroups
Changwen
Li
Xuzhou Normal University, XUZHOU, CHINA
Suppose $G$ is a finite group and $H$ is a subgroup of $G$. $H$ is said to be $s$-semipermutable in $G$ if $HG_{p} = G_{p}H$ for any Sylow $p$-subgroup $G_{p}$ of $G$ with $(p, |H|)=1$; $H$ is called weakly $s$-semipermutable in $G$ if there is a subgroup $T$ of $G$ such that $G=HT$ and $H\cap T$ is $s$-semipermutable in $G$. We investigate the influence of weakly $s$-semipermutable subgroups on the structure of finite groups. Some recent results are generalized and unified.
General
73
88
10.4171/RSMUP/126-5
http://www.ems-ph.org/doi/10.4171/RSMUP/126-5
Stabilité de l'holonomie sans structure de Frobenius: cas des courbes
Daniel
Caro
Université de Caen, CAEN CEDEX, FRANCE
By using Christol and Mebkhout's algebrization and finiteness theorem, we prove that in the case of smooth curves, Berthelot’s strongest conjecture on the stability of holonomicity is still valid without Frobenius structure but under some non-Liouville type hypotheses.
General
89
106
10.4171/RSMUP/126-6
http://www.ems-ph.org/doi/10.4171/RSMUP/126-6
Star Stability and Star Regularity for Mori Domains
Stefania
Gabelli
Università degli studi Roma Tre, ROMA, ITALY
Giampaolo
Picozza
Università degli studi Roma Tre, ROMA, ITALY
In the last few years, the concepts of stability and Clifford regularity have been fruitful extended by using star operations. In this paper we study and put in relation these properties for Noetherian and Mori domains, substantially improving several results present in the literature.
General
107
125
10.4171/RSMUP/126-7
http://www.ems-ph.org/doi/10.4171/RSMUP/126-7
Formal Extension of the Whitney Functor and Duality
Ana Rita
Martins
Universidade de Lisboa, LISBOA, PORTUGAL
Teresa
Monteiro Fernandes
Universidade de Lisboa, LISBOA, PORTUGAL
On a complex manifold we introduce the formal extension of the Whitney functor and the polynomial extension of the tempered cohomology functor, and prove a natural topological duality between them.
General
127
149
10.4171/RSMUP/126-8
http://www.ems-ph.org/doi/10.4171/RSMUP/126-8
Realization Theorems for Valuated $p^n$-Socles
Patrick
Keef
Whitman College, WALLA WALLA, UNITED STATES
If $n$ is a positive integer and $p$ is a prime, then a valuated $p^n$-socle is said to be $n$-summable if it is isometric to a valuated direct sum of countable valuated groups. The functions from $\omega_1$ to the cardinals that can appear as the Ulm function of an $n$-summable valuated $p^n$-socle are characterized, as are the $n$-summable valuated $p^n$-socles that can appear as the $p^n$-socle of some primary abelian group. The second statement generalizes a classical result of Honda from [9]. Assuming a particular consequence of the generalized continuum hypothesis, a complete description is given of the $n$-summable groups that are uniquely determined by their Ulm functions.
General
151
173
10.4171/RSMUP/126-9
http://www.ems-ph.org/doi/10.4171/RSMUP/126-9
On Riemann-Type Definition for the Wide Denjoy Integral
PIOTR
Sworowski
Casimirus the Great University, BYDGOSZCZ, POLAND
We give variational and Riemann-type definitions for some Lusin-type $\Delta$-continuous integrals being extensions of the wide Denjoy integral.
General
175
200
10.4171/RSMUP/126-10
http://www.ems-ph.org/doi/10.4171/RSMUP/126-10
Huppert's Conjecture for $Fi_{23}$
S.H.
Alavi
The University of Western Australia, CRAWLEY, WA, AUSTRALIA
A.
Daneshkah
Bu-Ali Sina University, HAMEDAN, IRAN
H.P.
Tong-Viet
University of KwaZulu-Natal, PIETERMARITZBURG, SOUTH AFRICA
T.P.
Wakefield
Youngstown State University, YOUNGSTOWN, UNITED STATES
Let $G$ denote a finite group and $\text{cd}(G)$ the set of irreducible character degrees of $G$. Bertram Huppert conjectured that if $H$ is a finite nonabelian simple group such that $\text{cd}(G) =\text{cd}(H)$, then $G\cong H \times A$, where $A$ is an abelian group. Huppert verified the conjecture for many of the sporadic simple groups. We illustrate the arguments by presenting the verification of Huppert's Conjecture for $Fi_{23}$.
General
201
211
10.4171/RSMUP/126-11
http://www.ems-ph.org/doi/10.4171/RSMUP/126-11
Which Fields Have No Maximal Subrings?
A.
Azarang
Chamran University, AHVAZ, IRAN
O.A.S.
Karamzadeh
Chamran University, AHVAZ, IRAN
Fields which have no maximal subrings are completely determined. We observe that the quotient fields of non-field domains have maximal subrings. It is shown that for each non-maximal prime ideal $P$ in a commutative ring $R$, the ring $R_P$ has a maximal subring. It is also observed that if $R$ is a commutative ring with $|Max(R)|>2^{\aleph_0}$ or $|R/J(R)|>2^{2^{\aleph_0}}$, then $R$ has a maximal subring. It is proved that the well-known and interesting property of the field of the real numbers $\mathbb{R}$ (i.e., $\mathbb{R}$ has only one nonzero ring endomorphism) is preserved by its maximal subrings. Finally, we characterize submaximal ideals (an ideal $I$ of a ring $R$ is called submaximal if the ring $R/I$ has a maximal subring) in the rings of polynomials in finitely many variables over any ring. Consequently, we give a slight generalization of Hilbert's Nullstellensatz.
General
213
228
10.4171/RSMUP/126-12
http://www.ems-ph.org/doi/10.4171/RSMUP/126-12
On Groups of Odd Order Admitting an Elementary 2-Group of Automorphisms
Karise
Oliveira
Ciência e Tecnologia de Goiás, INHUMAS GO, BRAZIL
Pavel
Shumyatsky
Universidade de Brasília, BRASILIA - DF, BRAZIL
Carmela
Sica
Università di Salerno, FISCIANO (SA), ITALY
Let $G$ be a finite group of odd order with derived length $k$. We show that if $G$ is acted on by an elementary abelian group $A$ of order $2^n$ and $C_G(A)$ has exponent $e$, then $G$ has a normal series $G=G_0\ge T_0\ge G_1\ge T_1\ge\cdots\ge G_n\ge T_n=1$ such that the quotients $G_i/T_i$ have $\{k,e,n\}$-bounded exponent and the quotients $T_i/G_{i+1}$ are nilpotent of $\{k,e,n\}$-bounded class.
General
229
236
10.4171/RSMUP/126-13
http://www.ems-ph.org/doi/10.4171/RSMUP/126-13
Generalized Dirac Operators on Lorentzian Manifolds and Propagation of Singularities
Paolo
Antonini
Faculté des Sciences d'Orsay, Orsay Cedex, FRANCE
We survey the correct definition of a generalized Dirac operator on a Space-Time and the classicla result about propagation of singularities. This says that light travels along light-like geodesics. Finally we show this is also true for generalized Dirac operators.
General
237
244
10.4171/RSMUP/126-14
http://www.ems-ph.org/doi/10.4171/RSMUP/126-14
Groups with all Subgroups Subnormal or Nilpotent-by-Chernikov
Howard
Smith
Bucknell University, LEWISBURG, UNITED STATES
General
245
253
10.4171/RSMUP/126-15
http://www.ems-ph.org/doi/10.4171/RSMUP/126-15