Enrico Savi

collaborators

5 papers

math.AG2026

Algebraic realization of stable PoincarÃ©-Reeb graphs

Enrico Savi

We introduce the notion of domain of finite type $D \subset R^{n}$ generalizing an earlier work of Bodin, Popescu-Pampu and Sorea. Then, we prove that every finite g…

math.AG2026

$K$ -holomorphic functions with definable real part

Antonio Carbone, Enrico Savi

Let $R$ be a real closed field and $K := R (i)$ its algebraic closure. Let $U \subset K^{n}$ be an open and definable set in a fixed o-minimal structure. In this note, we study the relat…

math.AG2026

On the first-order theories of quaternions and octonions

Enrico Savi

Let $L$ be the language of rings. We provide an axiomatization of the $L$ -theories of quaternions and octonions and characterize their models: they coincide, up to isomorphism, wit…

math.AG2025

The Nash-Tognoli theorem over the rationals and its version for isolated singularities

Riccardo Ghiloni, Enrico Savi

Let $Q$ be the field of rational numbers and let $X$ be a subset of $R^{n}$ . We say that $X$ is $Q$ -algebraic if it is the common zero set in $\mathbb{R}^n…

math.AG2025

A relative Nash-Tognoli theorem over $Q$ and application to the $Q$ -algebraicity problem

Enrico Savi

We prove a relative version over $Q$ of Nash-Tognoli theorem, that is: Let $M$ be a compact smooth manifold with closed smooth submanifolds $M_{1}, \dots, M_{ℓ}$ in general p…

Algebraic realization of stable PoincarÃ©-Reeb graphs

K-holomorphic functions with definable real part

On the first-order theories of quaternions and octonions

The Nash-Tognoli theorem over the rationals and its version for isolated singularities

A relative Nash-Tognoli theorem over Q and application to the Q-algebraicity problem

$K$ -holomorphic functions with definable real part

A relative Nash-Tognoli theorem over $Q$ and application to the $Q$ -algebraicity problem