Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.54 (2022)

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Sezione 1. Contributi

Kalliongis John, Ohashi Ryo

Orientation reversing finite abelian actions on RP³

Inglese Gabriele, Olmi Roberto

A note about the well-posedness of an Initial Boundary Value Problem for the heat equation in a layered domain

Dehimi Souheyb, Mortad Mohammed Hichem, Bachir Ahmed

Unbounded generalizations of the Fuglede-Putnam theorem

Lipparini Paolo

Products of sequentially compact spaces with no separability assumption

Hussein Sarbast, Benyoucef Salah

Analysis of existence and non-existence of limit cycles for a family of Kolmogorov systems

Alzer Horst, Kwong Man Kam

Monotonicity theorems and inequalities for certain sine sums

Sezione 2. TAGSS 2021 – Trieste Algebraic Geometry Summer School

Grosselli Gian Paolo, Spelta Irene

Explicit analysis of positive dimensional fibres of Pg,r and Xiao conjecture

Borówka Paweł, Ortega Angela

Prym varieties and Prym map

Izadi Elham, Canning Samir, Dutta Yajnaseni, Stapleton David

Hyperkähler manifolds

Sezione 3. Proceedings of the Go 60 Conference – Pure and Applied Algebraic Geomery celebrating Giorgio Ottaviani’s 60th birthday.

Ciliberto Ciro, Miranda Rick

Examples of non-effective rays at the boundary of the Mori cone of blow-ups of the plane

Portakal Irem, Sturmfels Bernd

Geometry of dependency equilibria

Abo Hirotachi, Lazarsfeld Robert, Smith Gregory G.

Ramification and discriminants of vector bundles and a quick proof of Bogomolov’s theorem

Lazić Vladimir, Schreyer Frank-olaf

Birational geometry and the canonical ring of a family of determinantal 3-folds

Chiantini Luca

On the study of decompositions of forms in four variables

Landsberg J.m.

Secant varieties and the complexity of matrix multiplication

Ng Kwing King Wayne, Vallès Jean

New examples of free projective curves

Boralevi Ada, Mezzetti Emilia

Pencils of singular quadrics of constant rank and their orbits

Biaggi Benjamin, Draisma Jan, Seynnaeve Tim

On the quadratic equations for odeco tensors

Fania Maria Lucia, Lanteri Antonio

Hilbert curves of quadric fibrations over smooth surfaces


Recent Submissions

Now showing 1 - 5 of 20
  • Publication
    Hilbert curves of quadric fibrations over smooth surfaces
    (EUT Edizioni Università di Trieste, 2022)
    Fania, Maria Lucia
    Lanteri, Antonio
    Let (X,L) be a complex polarized n-fold with the structure of a geometric quadric fibration over a smooth projective surface. The Hilbert curve of (X,L) is a complex affine plane curve of degree n, containing n − 3 evenly spaced parallel lines. This paper is devoted to a detailed study of the cubic representing the residual component. Reducibility, existence of triple points, and properties of the irreducible components are analyzed in connection with the structure of (X,L).
      49  118
  • Publication
    Monotonicity theorems and inequalities for certain sine sums
    (EUT Edizioni Università di Trieste, 2022)
    Alzer, Horst
    Kwong, Man Kam
    Inspired by the work of Askey-Steinig, Szeg\"o, and Schweitzer, we provide several monotonicity theorems and inequalities for certain sine sums. Among others, we prove that for $n\geq 1$ and $x\in (0,\pi/2)$, we have $$ \frac{d}{dx} \frac{C_n(x)}{1-\cos(x)}<0 \quad\mbox{and} \quad \frac{d}{dx} \left(1-\cos(x)\right)C_n(x)>0, $$ where $$ C_n(x)=\sum_{k=1}^n\frac{\sin((2k-1)x)}{2k-1} $$ denotes Carslaw's sine polynomial. Another result states that the inequality $$ \sum_{k=1}^n (n-k+a)(n-k+b) k \sin(kx)>0 \quad (a,b\in \mathbb{R}) $$ holds for all $n\geq 1$ and $x\in (0,\pi)$ if and only if $a=b=1$. Many corollaries and applications of these results are given. Among them, we present a two-parameter class of absolutely monotonic rational functions.
      53  128
  • Publication
    On the quadratic equations for odeco tensors
    (EUT Edizioni Università di Trieste, 2022)
    Biaggi, Benjamin
    Draisma, Jan
    Seynnaeve, Tim
    Elina Robeva discovered quadratic equations satisfied by orthogonally decomposable (“odeco”) tensors. Boralevi-Draisma-Emil Horobeț-Robeva then proved that, over the real numbers, these equations characterise odeco tensors. This raises the question to what extent they also characterise the Zariski-closure of the set of odeco tensors over the complex numbers. In the current paper we restrict ourselves to symmetric tensors of order three, i.e., of format n×n×n. By providing an explicit counterexample to one of Robeva’s conjectures, we show that for n ≥ 12, these equations do not suffice. Furthermore, in the open subset where the linear span of the slices of the tensor contains an invertible matrix, we show that Robeva’s equations cut out the limits of odeco tensors for dimension n ≤ 13, and not for n ≥ 14. To this end, we show that Robeva’s equations essentially capture the Gorenstein locus in the Hilbert scheme of n points and we use work by Casnati-Jelisiejew- Notari on the (ir)reducibility of this locus.
      48  94
  • Publication
    Pencils of singular quadrics of constant rank and their orbits
    (EUT Edizioni Università di Trieste, 2022)
    Boralevi, Ada
    Mezzetti, Emilia
    We give a geometric description of singular pencils of quadrics of constant rank, relating them to the splitting type of some naturally associated vector bundles on P1. Then we study their orbits in the Grassmannian of lines, under the natural action of the general linear group.
      71  150