43 citations · 150 across the 23 of their papers we have counts for
24 papers · 1 filter
On complete intersections of three quadrics in
Francesco Russo, Giovanni Staglianò
We describe explicit birational maps from some rational complete intersections of three quadrics in to some prime Fano manifolds together with their Sarkisov decompo…
Explicit computations with cubic fourfolds, Gushel-Mukai fourfolds, and their associated K3 surfaces
Giovanni Staglianò
We present some applications of the Macaulay2 software package SpecialFanoFourfolds, a package for working with Hodge-special cubic fourfolds and Hodge-special Gushel--Mukai fourfo…
Explicit constructions of K3 surfaces and unirational Noether-Lefschetz divisors
Michael Hoff, Giovanni Staglianò
We provide methods to construct explicit examples of surfaces. This leads to unirational constructions of Noether--Lefschetz divisors inside the moduli space of surfaces…
Computations with rational maps between multi-projective varieties
Giovanni Staglianò
We shortly describe the algorithms behind some of the functions provided by the Macaulay2 package MultiprojectiveVarieties, a package for multi-projective varieties and rational ma…
A package for computations with sparse resultants
Giovanni Staglianò
We introduce the Macaulay2 package SparseResultants, which provides general tools for computing sparse resultants, sparse discriminants, and hyperdeterminants. We give some backgro…
Some new rational Gushel fourfolds
Giovanni Staglianò
We provide explicit equations and parameterizations of some new rational Gushel-Mukai fourfolds of special type.
On some families of Gushel-Mukai fourfolds
Giovanni Staglianò
We give explicit descriptions of some Noether-Lefschetz divisors in the moduli space of Gushel-Mukai fourfolds. As a consequence we obtain that their Kodaira dimension is negative.
Algebraic boundaries among typical ranks for real binary forms of arbitrary degree
Maria Chiara Brambilla, Giovanni Staglianò
We show that the algebraic boundaries of the regions of real binary forms with fixed typical rank are always unions of dual varieties to suitable coincident root loci.
New examples of rational Gushel-Mukai fourfolds
Michael Hoff, Giovanni Staglianò
We construct new examples of rational Gushel-Mukai fourfolds, giving more evidence for the analog of the Kuznetsov Conjecture for cubic fourfolds: a Gushel--Mukai fourfold is ratio…
Trisecant Flops, their associated K3 surfaces and the rationality of some Fano fourfolds
Francesco Russo, Giovanni Staglianò
We provide a new construction of rationality for cubic fourfolds via Mori's theory and the minimal model program. As an application, we present the solution of the Kuznetsov's conj…
Special cubic birational transformations of projective spaces
Giovanni Staglianò
We extend our classification of special Cremona transformations whose base locus has dimension at most three to the case when the target space is replaced by a (locally) factorial…
Explicit rationality of some cubic fourfolds
Francesco Russo, Giovanni Staglianò
Recent results of Hassett, Kuznetsov and others pointed out countably many divisors in the open subset of par…
On the algebraic boundaries among typical ranks for real binary forms
Maria Chiara Brambilla, Giovanni Staglianò
We describe the algebraic boundaries of the regions of real binary forms with fixed typical rank and of degree at most eight, showing that they are dual varieties of suitable coinc…
Hypersurfaces with vanishing hessian via Dual Cayley Trick
Rodrigo Gondim, Francesco Russo, Giovanni Staglianò
We present a general construction of hypersurfaces with vanishing hessian, starting from any irreducible non-degenerate variety whose dual variety is a hypersurface and based on th…
Congruences of 5-secant conics and the rationality of some admissible cubic fourfolds
Francesco Russo, Giovanni Staglianò
The works of Hassett and Kuznetsov identify countably many divisors in the open subset of parametrizing all c…
A package for computations with classical resultants
Giovanni Staglianò
We present the Macaulay2 package Resultants, which provides commands for the effective computation of multivariate resultants, discriminants, and Chow forms. We provide some backgr…
Effective identifiability criteria for tensors and polynomials
Alex Massarenti, Massimiliano Mella, Giovanni Staglianò
A tensor , in a given tensor space, is said to be -identifiable if it admits a unique decomposition as a sum of rank one tensors. A criterion for -identifiability is c…
A Macaulay2 package for computations with rational maps
Giovanni Staglianò
The Macaulay2 package Cremona performs some computations on rational and birational maps between irreducible projective varieties. For instance, it provides methods to compute degr…
Special cubic Cremona transformations of and
Giovanni Staglianò
A famous result of B. Crauder and S. Katz (1989) concerns the classification of special Cremona transformations whose base locus has dimension at most two. Furthermore, they also p…
Some Loci of Rational Cubic Fourfolds
Michele Bolognesi, Francesco Russo, Giovanni Staglianò
In this paper we investigate the divisor inside the moduli space of smooth cubic hypersurfaces in , whose generic element is a smooth cubic containin…
Examples of special quadratic birational transformations into complete intersections of quadrics
Giovanni Staglianò
In our previous works (2012, 2013), we provided a finite list of properties characterizing all potential types of quadratic birational transformations of a projective space into a…
On special quadratic birational transformations of a projective space
Giovanni Staglianò
A birational map from a projective space onto a not too much singular projective variety with a single irreducible non-singular base locus scheme (special birational transformation…
On special quadratic birational transformations whose base locus has dimension at most three
Giovanni Staglianò
We study birational transformations P^n--->S \subseteq P^N defined by linear systems of quadrics whose base locus is smooth and irreducible of dimension \leq3 and whose image S is…
On special quadratic birational transformations of a projective space into a hypersurface
Giovanni Staglianò
We study transformations as in the title with emphasis on those having smooth connected base locus, called "special". In particular, we classify all special quadratic birational ma…