Alex Massarenti

activity

20102026

most citedExplicit log Fano structures on blow-ups of projective spaces

34 citations · 139 across the 44 of their papers we have counts for

collaborators

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52 papers · 1 filter

math.AG2026

Unirational Fano threefolds

Alex Massarenti

We use the relative Abel--Jacobi construction of Cheltsov--Loginov--Orlov--Prokhorov to study unirational Fano threefolds. Our main result is a $50$ -dimensional family of smooth un…

math.AG2026

Mori theory and symplectic reduction for polygons and quivers

Alessia Mandini, Alex Massarenti

We investigate the birational geometry of moduli spaces of polygons and quivers, emphasizing the link between Mori theory and symplectic reduction. On the additive side we relate M…

math.AG2026

Quadratic Cremona transformations of $P^{4}$

Gianluca Grassi, Alex Massarenti

We prove that $B i r_{2} (P^{4})$ has exactly nine irreducible components and that the locus of transformations with zero-dimensional base scheme is irreducible.

math.AG2026

Log-Conformal Projective Manifolds

Maurício Corrêa, Alex Massarenti

Let $(X, Δ)$ be a smooth complex projective simple normal crossing pair of dimension $n \geq 3$ endowed with an everywhere nondegenerate logarithmic conformal tensor. If $K_{X} + Δ$ is no…

math.AG2026

Compactifications of spaces of symmetric matrices and pointed Kontsevich spaces of isotropic Grassmannians

Hanlong Fang, Alex Massarenti, Xian Wu

We study two closely related families of varieties arising from genus $0$ stable maps to the Lagrangian Grassmannian $LG (n, 2 n)$ . First, we construct the Kausz--type…

math.AG2026

Canonical blow-ups of Lagrangian and Orthogonal Grassmannians

Hanlong Fang, Alex Massarenti, Xian Wu

Let $LG (V \oplus V^{*})$ and $OG^{+} (V \oplus V^{*})$ denote the Lagrangian and orthogonal Grassmannians endowed with the natural $G_{m}$ -actions, respectively. Th…

math.AG2025

On the unirationality of conic bundles with discriminant of degree eight

Alex Casarotti, Søren Gammelgaard, Alex Massarenti

We study the unirationality of surface conic bundles $π : S \to P^{1}$ over an arbitrary field $k$ with discriminant degree $d_{S} = 8$ , the first case beyond the del Pezzo ran…

math.AG2025

The Alexander-Hirschowitz theorem for neurovarieties

A. Massarenti, M. Mella

We study the dimension and identifiability of neurovarieties associated to polynomial neural networks. We give an independent geometric proof that the linear bounds $d_i\geq 2n_i-1…

math.AG2025

On K-stability of Fano's last Fanos

Ivan Cheltsov, DongSeon Hwang, Alex Küronya +5

We study K-stability of smooth Fano threefolds of Picard rank $2$ and degree $22$ which can be obtained by blowing up a smooth complete intersection of two quadrics in $\mathbb{P}^…

math.AG2025

Algebraic growth of the Cremona group

Alberto Calabri, Serge Cantat, Alex Massarenti +2

We initiate the study of the ''algebraic growth'' of groups of automorphisms and birational transformations of algebraic varieties. Our main result concerns $\text{Bir}(\mathbb{P}^…

math.AG2024

Mori dream singular $K 3$ surfaces

Antonio Laface, Alex Massarenti, William D. Montoya

We take a first step towards the classification of singular Mori dream $K 3$ surfaces. We prove that if the Picard lattice of a singular $K 3$ surface is Mori dream, then the surface…

math.AG2024

The moduli space of genus $8$ Fano $3$ -folds with two $\frac{1}{2} (1, 1, 1)$ -points: rationality and K-stability

Joseph Malbon, Alex Massarenti, Francesco Zucconi

Let $F_{8, 2 \times \frac{1}{2} (1, 1, 1)}$ be the moduli space of genus $8$ Fano $3$ -folds with two terminal quotient singularities of type $\frac{1}{2} (1, 1, 1)$ . We prove that $\mathca…

math.AG2024

Rational points on even dimensional Fermat cubics

Alex Massarenti

We show that even dimensional Fermat cubic hypersurfaces are rational over any field of characteristic different from three by producing explicit rational parametrizations given by…

math.AG2023

Cox rings of blow-ups of multiprojective spaces

Michele Bolognesi, Alex Massarenti, Elena Poma

Let $X_{r}^{1, n}$ be the blow-up of $P^{1} \times P^{n}$ in $r$ general points. We describe the Mori cone of $X_{r}^{1, n}$ for $r \leq n + 2$ and for $r = n + 3$ when $n \leq 4$ .…

math.AG2023

Birational geometry of Calabi-Yau pairs and 3-dimensional Cremona transformations

Carolina Araujo, Alessio Corti, Alex Massarenti

We develop a framework that allows one to describe the birational geometry of Calabi-Yau pairs $(X, D)$ . After establishing some general results for Calabi-Yau pairs $(X, D)$ with mi…

math.AG2023★ 3 cited

Ample bodies and Terracini loci of projective varieties

Antonio Laface, Alex Massarenti

We introduce the notion of ample body of a projective variety and use it to prove emptiness results for Terracini loci and specific identifiability results for toric and homogeneou…

math.AG2022

Quartic and Quintic hypersurfaces with dense rational points

Alex Massarenti

Let $X_{4} \subset P^{n + 1}$ be a quartic hypersurface of dimension $n \geq 4$ over an infinite field $k$ . We show that if either $X_{4}$ contains a linear subspace $Λ$ of dimensi…

math.AG2022★ 1 cited

Bronowski's conjecture and the identifiability of projective varieties

Alex Massarenti, Massimiliano Mella

Let $X \subset P^{hn + h - 1}$ be an irreducible and non-degenerate variety of dimension $n$ . The Bronowski's conjecture predicts that $X$ is $h$ -identifiable if and only if the…

math.AG2022

On the unirationality of quadric bundles

Alex Massarenti

We prove that a general $n$ -fold quadric bundle $Q^{n - 1} \to P^{1}$ , over a number field, with $(- K_{Q^{n - 1}})^{n} > 0$ and discriminant of odd deg…

math.AG2021

Complete singular collineations and quadrics

Alex Casarotti, Elsa Corniani, Alex Massarenti

We construct wonderful compactifications of the spaces of linear maps, and symmetric linear maps of a given rank as blow-ups of secant varieties of Segre and Veronese varieties. Fu…

math.AG2021

On the birational geometry of conic bundles over the projective space

Alex Massarenti, Massimiliano Mella

Let $π : Z \to P^{n - 1}$ be a general minimal $n$ -fold conic bundle with a hypersurface $B_{Z} \subset P^{n - 1}$ of degree $d$ as discriminant. We prove that if $d\…

math.AG2021

Decomposition algorithms for tensors and polynomials

Antonio Laface, Alex Massarenti, Rick Rischter

We give algorithms to compute decompositions of a given polynomial, or more generally mixed tensor, as sum of rank one tensors, and to establish whether such a decomposition is uni…

math.AG2020

Complete symplectic quadrics and Kontsevich spaces of conics in Lagrangian Grassmannians

Elsa Corniani, Alex Massarenti

A wonderful compactification of an orbit under the action of a semi-simple and simply connected group is a smooth projective variety containing the orbit as a dense open subset, an…

math.AG2020

On the weak Lefschetz principle in birational geometry

César Lozano Huerta, Alex Massarenti

This is an expository article written for the Notices of the AMS in which we discuss the weak Lefschetz Principle in birational geometry. Our departing point is the influential wor…

Unirational Fano threefolds

Mori theory and symplectic reduction for polygons and quivers

Quadratic Cremona transformations of P4

Log-Conformal Projective Manifolds

Compactifications of spaces of symmetric matrices and pointed Kontsevich spaces of isotropic Grassmannians

Canonical blow-ups of Lagrangian and Orthogonal Grassmannians

On the unirationality of conic bundles with discriminant of degree eight

The Alexander-Hirschowitz theorem for neurovarieties

On K-stability of Fano's last Fanos

Algebraic growth of the Cremona group

Mori dream singular K3 surfaces

The moduli space of genus 8 Fano 3-folds with two 21​(1,1,1)-points: rationality and K-stability

Rational points on even dimensional Fermat cubics

Cox rings of blow-ups of multiprojective spaces

Birational geometry of Calabi-Yau pairs and 3-dimensional Cremona transformations

Ample bodies and Terracini loci of projective varieties

Quartic and Quintic hypersurfaces with dense rational points

Bronowski's conjecture and the identifiability of projective varieties

On the unirationality of quadric bundles

Complete singular collineations and quadrics

On the birational geometry of conic bundles over the projective space

Decomposition algorithms for tensors and polynomials

Complete symplectic quadrics and Kontsevich spaces of conics in Lagrangian Grassmannians

On the weak Lefschetz principle in birational geometry

Quadratic Cremona transformations of $P^{4}$

Mori dream singular $K 3$ surfaces

The moduli space of genus $8$ Fano $3$ -folds with two $\frac{1}{2} (1, 1, 1)$ -points: rationality and K-stability