59 citations · 129 across the 20 of their papers we have counts for
21 papers · 1 filter
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 , of the Stanley-Reisner ring $S_{\mathcal{K…
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 . We prove that its boundary, which parametrizes singular members, is purely divisorial and c…
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 subschemes of at the point corresponding to the ideal $\langle x_1,\ldots,x_n\rangl…
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…
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…
Reflexive polygons and rational elliptic surfaces
Antonella Grassi, Giulia Gugiatti, Wendelin Lutz +1
In this note we study in detail the geometry of eight rational elliptic surfaces naturally associated to the sixteen reflexive polygons. The elliptic fibrations supported by these…
On K-moduli of quartic threefolds
Hamid Abban, Ivan Cheltsov, Alexander Kasprzyk +2
The family of smooth Fano 3-folds with Picard rank 1 and anticanonical volume 4 consists of quartic 3-folds and of double covers of the 3-dimensional quadric branched along an octi…
Deformations of log Calabi-Yau pairs can be obstructed
Simon Felten, Andrea Petracci, Sharon Robins
We exhibit examples of pairs where is a smooth projective variety and is an anticanonical reduced simple normal crossing divisor such that the deformations of $(X,D…
K-moduli of Fano 3-folds can have embedded points
Andrea Petracci
We exhibit an example of obstructed K-polystable Fano 3-fold such that the K-moduli stack of K-semistable Fano varieties and the K-moduli space of K-polystable Fano varieties h…
On deformation spaces of toric singularities and on singularities of K-moduli of Fano varieties
Andrea Petracci
Firstly, we see that the bases of the miniversal deformations of isolated -Gorenstein toric singularities are quite restricted. In particular, we classify the analytic…
A 1-dimensional component of K-moduli of del Pezzo surfaces
Andrea Petracci
We explicitly construct a component of the K-moduli space of K-polystable del Pezzo surfaces which is a smooth rational curve.
On K-stability of some del Pezzo surfaces of Fano index 2
Yuchen Liu, Andrea Petracci
For every integer , we relate the K-stability of hypersurfaces in the weighted projective space of degree with the GIT stability of binary form…
The logarithmic Bogomolov-Tian-Todorov theorem
Simon Felten, Andrea Petracci
We prove that the log smooth deformations of a proper log smooth saturated log Calabi-Yau space are unobstructed.
On toric geometry and K-stability of Fano varieties
Anne-Sophie Kaloghiros, Andrea Petracci
We present some applications of the deformation theory of toric Fano varieties to K-(semi/poly)stability of Fano varieties. First, we present two examples of K-polystable toric Fan…
Mirror Symmetry and smoothing Gorenstein toric affine 3-folds
Alessio Corti, Matej Filip, Andrea Petracci
We state two conjectures that together allow one to describe the set of smoothing components of a Gorenstein toric affine 3-fold in terms of a combinatorially defined and easily st…
On deformations of toric Fano varieties
Andrea Petracci
In this note we collect some results on the deformation theory of toric Fano varieties.
An example of Mirror Symmetry for Fano threefolds
Andrea Petracci
In this note we illustrate the Fanosearch programme of Coates, Corti, Galkin, Golyshev, and Kasprzyk in the example of the anticanonical cone over the smooth del Pezzo surface of d…
Some examples of non-smoothable Gorenstein Fano toric threefolds
Andrea Petracci
We present a combinatorial criterion on reflexive polytopes of dimension 3 which gives a local-to-global obstruction for the smoothability of the corresponding Fano toric threefold…
Homogeneous deformations of toric pairs
Andrea Petracci
We extend the Altmann--Mavlyutov construction of homogeneous deformations of affine toric varieties to the case of toric pairs , where is an affine or projecti…
On the quantum periods of del Pezzo surfaces with singularities
Alessandro Oneto, Andrea Petracci
In earlier joint work with our collaborators Akhtar, Coates, Corti, Heuberger, Kasprzyk, Prince and Tveiten, we gave a conjectural classification of a broad class of orbifold del P…
Mirror Symmetry and the Classification of Orbifold del Pezzo Surfaces
Mohammad Akhtar, Tom Coates, Alessio Corti +6
We state a number of conjectures that together allow one to classify a broad class of del Pezzo surfaces with cyclic quotient singularities using mirror symmetry. We prove our conj…