Andrea T. Ricolfi

activity

20152026

most citedHigher rank K-theoretic Donaldson-Thomas theory of points

22 citations · 123 across the 28 of their papers we have counts for

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34 papers · 1 filter

math.AG2026

Derived supergeometry and perfect obstruction theories on algebraic superstacks

Ugo Bruzzo, Daniel Hernández Ruipérez, Emanuele Pavia +1

We develop a deformation-theoretic framework for algebraic superstacks and apply it to the construction of perfect obstruction theories on moduli spaces of stable supermaps. In ord…

math.AG2026

Motivic and cohomological stabilisation of the Quot scheme of points

Michele Graffeo, Alexis Aumonier, Sergej Monavari +2

We prove that the motive of the punctual Quot scheme $Quot^{d} (O_{A^{n}}^{\oplus r})_{0}$ stabilises, when $n \to \infty$ , to $[\mathrm{Gr}(d-1,\infty)]\cdot \s…

math.AG2025

Deformation theory for a morphism in the derived category with fixed lift of the codomain

Pieter Belmans, Wendy Lowen, Shinnosuke Okawa +1

We develop the deformation-obstruction calculus for morphisms of complexes with a fixed lift of the codomain, to derived categories of flat nilpotent deformations of abelian catego…

math.AG2025

Invariants of nested Hilbert and Quot schemes on surfaces

Nadir Fasola, Michele Graffeo, Danilo Lewański +1

Let $(S, p)$ be a smooth pointed surface. In the first part of this paper we study motivic invariants of punctual nested Hilbert schemes attached to $(S, p)$ using the Hilbert-Samuel…

math.AG2024

Derived hyperquot schemes

Sergej Monavari, Emanuele Pavia, Andrea T. Ricolfi

We define a derived enhancement of the hyperquot scheme (also known as nested Quot scheme), which classically parametrises flags of quotients of a perfect coherent sheaf on a proje…

math.AG2024★ 2 cited

The motive of the Hilbert scheme of points in all dimensions

Michele Graffeo, Sergej Monavari, Riccardo Moschetti +1

We prove a closed formula for the generating function $Z_{d} (t)$ of the motives $[Hilb^{d} (A^{n})_{0}] \in K_{0} (Var_{C})$ of punctual Hilbert schem…

math.AG2024

On the stack of 0-dimensional coherent sheaves: structural aspects

Barbara Fantechi, Andrea T. Ricolfi

Let $X$ be a quasiprojective scheme. In this expository note we collect a series of useful structural results on the stack $C o h^{n} (X)$ parametrising $0$ -dimensional cohere…

math.AG2024★ 5 cited

Hyperquot schemes on curves: virtual class and motivic invariants

Sergej Monavari, Andrea T. Ricolfi

Let $C$ be a smooth projective curve, $E$ a locally free sheaf. Hyperquot schemes on $C$ parametrise flags of coherent quotients of $E$ with fixed Hilbert polynomial, and offer alt…

math.AG2024

On the stack of 0-dimensional coherent sheaves: motivic aspects

Barbara Fantechi, Andrea T. Ricolfi

Let $X$ be a variety. In this survey, we study (decompositions of) the motivic class, in the Grothendieck ring of stacks, of the stack $C o h^{n} (X)$ of $0$ -dimensional coher…

math.AG2023★ 3 cited

The geometry of double nested Hilbert schemes of points on curves

Michele Graffeo, Paolo Lella, Sergej Monavari +2

Let $C$ be a smooth curve. In this paper we investigate the geometric properties of the double nested Hilbert scheme of points on $C$ , a moduli space introduced by the third author…

math.AG2023

A sign that used to annoy me, and still does

Andrea T. Ricolfi

We provide a proof of the following fact: if a complex scheme $Y$ has Behrend function constantly equal to a sign $σ \in {\pm 1}$ , then all of its components $Z \subset Y$ are gen…

math.AG2023

Motivic classes of noncommutative Quot schemes

Andrea T. Ricolfi

We provide a recursive formula for the motivic class of the noncommutative Quot scheme in the Grothendieck ring of stacks.

math.AG2022

Hilbert squares of degeneracy loci

Enrico Fatighenti, Francesco Meazzini, Giovanni Mongardi +1

Let $S$ be the first degeneracy locus of a morphism of vector bundles corresponding to a general matrix of linear forms in $P^{s}$ . We prove that, under certain positivity c…

math.AG2022

On the Behrend function and the blowup of some fat points

Michele Graffeo, Andrea T. Ricolfi

The Behrend function of a $C$ -scheme $X$ is a constructible function $ν_{X} : X (C) \to Z$ introduced by Behrend, intrinsic to the scheme structure of $X$ .…

math.AG2021

Sur la lissité du schéma Quot ponctuel emboîté

Sergej Monavari, Andrea T. Ricolfi

In this paper we characterise the smoothness of the nested Quot scheme of points of a smooth variety, namely the moduli space parametrising flags of $0$ -dimensional quotients of a…

math.AG2021★ 1 cited

The d-critical structure on the Quot scheme of points of a Calabi-Yau 3-fold

Andrea T. Ricolfi, Michail Savvas

The Artin stack $M_{n}$ of $0$ -dimensional sheaves of length $n$ on $A^{3}$ carries two natural d-critical structures in the sense of Joyce. One comes from its descrip…

math.AG2021★ 21 cited

On the motive of the nested Quot scheme of points on a curve

Sergej Monavari, Andrea T. Ricolfi

Let $C$ be a smooth curve over an algebraically closed field $k$ , and let $E$ be a locally free sheaf of rank $r$ . We compute, for every $d > 0$ , the generating function of…

math.AG2020

Indecomposability of derived categories in families

Francesco Bastianelli, Pieter Belmans, Shinnosuke Okawa +1

Using the moduli space of semiorthogonal decompositions in a smooth projective family, introduced by the second, the third and the fourth author, we propose a novel approach to ind…

math.AG2020★ 2 cited

Higher rank motivic Donaldson-Thomas invariants of $A^{3}$ via wall-crossing, and asymptotics

Alberto Cazzaniga, Dimbinaina Ralaivaosaona, Andrea T. Ricolfi

We compute, via motivic wall-crossing, the generating function of virtual motives of the Quot scheme of points on $A^{3}$ , generalising to higher rank a result of Behrend, B…

math.AG2020

Framed sheaves on projective space and Quot schemes

Alberto Cazzaniga, Andrea T. Ricolfi

We prove that, given integers $m \geq 3$ , $r \geq 1$ and $n \geq 0$ , the moduli space of torsion free sheaves on $P^{m}$ with Chern character $(r, 0, \dots, 0, - n)$ that are trivia…

math.AG2020★ 1 cited

Framed motivic Donaldson-Thomas invariants of small crepant resolutions

Alberto Cazzaniga, Andrea T. Ricolfi

For an arbitrary integer $r \geq 1$ , we compute $r$ -framed motivic PT and DT invariants of small crepant resolutions of toric Calabi-Yau $3$ -folds, establishing a "higher rank" vers…

math.AG2020

The equivariant Atiyah class

Andrea T. Ricolfi

Let $X$ be a complex scheme acted on by an affine algebraic group $G$ . We prove that the Atiyah class of a $G$ -equivariant perfect complex on $X$ , as constructed by Huybrechts and…

math.AG2020★ 22 cited

Higher rank K-theoretic Donaldson-Thomas theory of points

Nadir Fasola, Sergej Monavari, Andrea T. Ricolfi

We exploit the critical locus structure on the Quot scheme $Quot_{A^{3}} (O^{\oplus r}, n)$ , in particular the associated symmetric obstruction theory, in ord…

math.AG2020★ 7 cited

Moduli spaces of semiorthogonal decompositions in families

Pieter Belmans, Shinnosuke Okawa, Andrea T. Ricolfi

To a smooth and proper morphism $X \to U$ with quasicompact semiseparated target we associate a sheaf in the étale topology, which takes an affine $U$ -scheme $V$ to the se…

Derived supergeometry and perfect obstruction theories on algebraic superstacks

Motivic and cohomological stabilisation of the Quot scheme of points

Deformation theory for a morphism in the derived category with fixed lift of the codomain

Invariants of nested Hilbert and Quot schemes on surfaces

Derived hyperquot schemes

The motive of the Hilbert scheme of points in all dimensions

On the stack of 0-dimensional coherent sheaves: structural aspects

Hyperquot schemes on curves: virtual class and motivic invariants

On the stack of 0-dimensional coherent sheaves: motivic aspects

The geometry of double nested Hilbert schemes of points on curves

A sign that used to annoy me, and still does

Motivic classes of noncommutative Quot schemes

Hilbert squares of degeneracy loci

On the Behrend function and the blowup of some fat points

Sur la lissité du schéma Quot ponctuel emboîté

The d-critical structure on the Quot scheme of points of a Calabi-Yau 3-fold

On the motive of the nested Quot scheme of points on a curve

Indecomposability of derived categories in families

Higher rank motivic Donaldson-Thomas invariants of A3 via wall-crossing, and asymptotics

Framed sheaves on projective space and Quot schemes

Framed motivic Donaldson-Thomas invariants of small crepant resolutions

The equivariant Atiyah class

Higher rank K-theoretic Donaldson-Thomas theory of points

Moduli spaces of semiorthogonal decompositions in families

Higher rank motivic Donaldson-Thomas invariants of $A^{3}$ via wall-crossing, and asymptotics