Andrea Petracci

activity

20242026

collaborators

7 papers

math.AG2026

Higher cotangent cohomology for Stanley-Reisner rings

Nathan Ilten, Francesco Meazzini, Andrea Petracci

Inspired by work of Altmann and Christophersen, we study the graded pieces of the cotangent cohomology $T_{S_{K}}^{i}$ , $i \geq 3$ of the Stanley-Reisner ring $S_{\mathcal{K…

math.AG2026

The boundary of K-moduli of prime Fano threefolds of genus twelve

Anne-Sophie Kaloghiros, Yuchen Liu, Andrea Petracci +1

We study the K-moduli stack of prime Fano threefolds of genus twelve, known as $V_{22}$ . We prove that its boundary, which parametrizes singular members, is purely divisorial and c…

math.AG2025

Local Equations for Hilbert Schemes of Points

Nathan Ilten, Francesco Meazzini, Andrea Petracci

We compute the completion of the local ring of the Hilbert scheme of degree $n + 1$ subschemes of $A^{n}$ at the point corresponding to the ideal $\langle x_1,\ldots,x_n\rangl…

math.AG2025

K-moduli of Fano 3-folds can have embedded points

Andrea Petracci

We exhibit an example of obstructed K-polystable Fano 3-fold $X$ such that the K-moduli stack of K-semistable Fano varieties and the K-moduli space of K-polystable Fano varieties h…

math.AG2024

Smoothing Gorenstein toric Fano 3-folds

Alessio Corti, Paul Hacking, Andrea Petracci

We introduce admissible Minkowski decomposition data (amd) for a 3-dimensional reflexive polytope P. This notion is defined purely in terms of the combinatorics of P. Denoting by X…

math.AG2024

On K-moduli of Fano threefolds with degree 28 and Picard rank 4

Liana Heuberger, Andrea Petracci

We analyse the local structure of the K-moduli space of Fano varieties at a toric singular K-polystable Fano 3-fold, which deforms to smooth Fano 3-folds with anticanonical volume…