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Anna Gori

Publications and source records attributed to Anna Gori.

At least 19 recordsLinked to original sources
arXiv2026

A note on irreducible slice algebraic sets

In this short note we prove that if $I$ is a right radical and quasi prime ideal in the ring of quaternionic slice regular polynomials, then the symmetrization $\mathbb S_{V_c(I)}$ is an irreducible algebraic set, where $V_c(I)$ is the set of common zeros with commuting components of polynomials in $I$. Combining this fact with the results proved in our previous paper [3], we obtain that for $I$ radical, $V_c(I)$ is irreducible if and only if $I$ is quasi prime.

math.AG↗
arXiv2025

A Strong Version of the Hilbert Nullstellensatz for slice regular polynomials in several quaternionic variables

In this paper we prove a strong version of the Hilbert Nullstellensatz in the ring $\mathbb H[q_1,\ldots,q_n]$ of slice regular polynomials in several quaternionic variables. Our proof deeply depends on a detailed analysis of the common zeros of slice regular polynomials which belong to an ideal in $\mathbb H[q_1,\ldots,q_n]$. This study motivates the introduction of a new notion of algebraic set in the quaternionic setting, which allows us to define a Zariski-type topology on $\mathbb H^n$.

math.CV↗
arXiv2025

On the irreducibility of slice algebraic sets

In the present paper we investigate the relations between irreducible slice algebraic sets in $\mathbb{H}^n$ and quasi prime right ideals of the ring of slice regular polynomials in $n$ quaternionic variables. We provide algebraic conditions on right ideals of slice regular polynomials which guarantee the irreducibility of the corresponding slice algebraic sets and show that radical ideals associated with irreducible slice algebraic sets are quasi prime. Furthermore we establish that this correspondence is an equivalence in the case of principal right ideals.

math.AG↗
arXiv2019

On compact affine quaternionic curves and surfaces

This paper is devoted to the study of affine quaternionic manifolds and to a possible classification of all compact affine quaternionic curves and surfaces. It is established that on an affine quaternionic manifold there is one and only one affine quaternionic structure. A direct result, based on the celebrated Kodaira Theorem that studies compact complex manifolds in complex dimension 2, states that the only compact affine quaternionic curves are the quaternionic tori and the primary Hopf surface S^3 x S^1. As for compact affine quaternionic surfaces, we restrict to the complete ones: the study of their fundamental groups, together with the inspection of all nilpotent hypercomplex simply connected 8-dimensional Lie Groups, identifies a path towards their classification.

math.DG↗
arXiv2016

Quaternionic toric manifolds

In the present paper we introduce and study a new notion of toric manifold in the quaternionic setting. We develop a construction with which, starting from appropriate $m$-dimensional Delzant polytopes, we obtain manifolds of real dimension $4m$, acted on by $m$ copies of the group ${\rm Sp}(1)$ of unit quaternions. These manifolds are quaternionic regular and can be endowed with a $4$-plectic structure and a generalized moment map. Convexity properties of the image of the moment map are studied. Quaternionic toric manifolds appear to be a large enough class of examples where one can test and study new results in quaternionic geometry.

math.DG↗
arXiv2016

A direct approach to quaternionic manifolds

The recent definition of slice regular function of several quaternionic variables suggests a new notion of quaternionic manifold. We give the definition of quaternionic regular manifold, as a space locally modeled on $\mathbb{H}^n$, in a slice regular sense. We exhibit some significant classes of examples, including manifolds which carry a quaternionic affine structure.

math.CV↗
arXiv2006

Homogeneous Lagrangian submanifolds

We characterize isometric actions on compact Kaehler manifolds admitting a Lagrangian orbit, describing under which condition the Lagrangian orbit is unique. We furthermore give the complete classification of simple groups acting on the complex projective space with a Lagrangian orbit, and we give the explicit list of these orbits.

math.DG↗
arXiv2005

On deformations of Hamiltonian actions

In this paper we generalize to coisotropic actions of compact Lie groups a theorem of Guillemin on deformations of Hamiltonian structures on compact symplectic manifolds. We show how one can reconstruct from the moment polytope the symplectic form on the manifold.

math.SG↗
arXiv2004

A splitting result for compact symplectic manifolds

We consider compact symplectic manifolds acted on effectively by a compact connected Lie group $K$ in a Hamiltonian fashion. We prove that the squared moment map $||μ||^2$ is constant if and only if $K$ is semisimple and the manifold is $K$-equivariantly symplectomorphic to a product of a flag manifold and a compact symplectic manifold which is acted on trivially by $K$. In the almost-Kähler setting the symplectomorphism turns out to be an isometry.

math.SG↗
arXiv2004

Complex Asystatic actions of compact Lie Groups

In the present paper we introduce the notion of complex asystatic Hamiltonian action on a Kähler manifold. In the algebraic setting we prove that if a complex linear group $G$ acts complex asystatically on a Kähler manifold then the $G$-orbits are spherical. Finally we give the complete classification of complex asystatic irreducible representations.

math.DG↗
arXiv2003

A note on the moment map on compact Kähler manifolds

We consider compact Kähler manifolds acted on by a connected compact Lie group $K$ of isometries in Hamiltonian fashion. We prove that the squared moment map $\|μ\|^2$ is constant if and only if the manifold is biholomorphically and $K$-equivariantly isometric to a product of a flag manifold and a compact Kähler manifold which is acted on trivially by $K$. The authors do not know whether the compactness of $M$ is essential in the main theorem; more generally it would be interesting to have a similar result for (compact) symplectic manifolds.

math.SG↗
arXiv2003

Two-orbit Kähler manifolds and Morse Theory

We deal with compact Kähler manifolds $M$ acted on by a compact Lie group $K$ of isometries, whose complexification $K^\C$ has exactly one open and one closed orbit in $M$. If the $K$-action is Hamiltonian, we obtain results on the cohomology and the $K$-equivariant cohomology of $M$.

math.SG↗