16 citations · 111 across the 28 of their papers we have counts for
29 papers · 1 filter
The hyperkähler period-index conjecture is false
Pieter Belmans, James Hotchkiss
Huybrechts conjectured that for every Brauer class on a hyperkähler variety we have that , strengthening the usual p…
Central curves on noncommutative surfaces
Thilo Baumann, Pieter Belmans, Okke van Garderen
There exists a dictionary between hereditary orders and smooth stacky curves, resp. tame orders of global dimension 2 and Azumaya algebras on smooth stacky surfaces. We extend this…
On decompositions for Fano schemes of intersections of two quadrics
Pieter Belmans, Jishnu Bose, Sarah Frei +6
We propose conjectural semiorthogonal decompositions for Fano schemes of linear subspaces on intersections of two quadrics, in terms of symmetric powers of the associated hyperelli…
Hochschild cohomology of Hilbert schemes of points on surfaces
Pieter Belmans, Lie Fu, Andreas Krug
We compute the Hochschild cohomology of Hilbert schemes of points on surfaces and observe that it is, in general, not determined solely by the Hochschild cohomology of the surface,…
On Chow rings of quiver moduli
Pieter Belmans, Hans Franzen
We describe the point class and Todd class in the Chow ring of a quiver moduli space, building on a result of Ellingsrud-Strømme. This, together with the presentation of the Chow r…
Projectivity and effective global generation of determinantal line bundles on quiver moduli
Pieter Belmans, Chiara Damiolini, Hans Franzen +3
We give a moduli-theoretic treatment of the existence and properties of moduli spaces of semistable quiver representations, avoiding methods from geometric invariant theory. Using…
Graph potentials and symplectic geometry of moduli spaces of vector bundles
Pieter Belmans, Sergey Galkin, Swarnava Mukhopadhyay
We give the first examples of Fano manifolds with multiple optimal tori, i.e.~we construct monotone Lagrangian tori , such that the weighted number of holomorphic Maslov index t…
Projectivity of the moduli space of vector bundles on a curve
Jarod Alper, Pieter Belmans, Daniel Bragg +2
We discuss the projectivity of the moduli space of semistable vector bundles on a curve of genus . This is a classical result from the 1960s, obtained using geometric inva…
Graph potentials and topological quantum field theories
Pieter Belmans, Sergey Galkin, Swarnava Mukhopadhyay
We introduce graph potentials, which are Laurent polynomials associated to (colored) trivalent graphs. We show that the birational type of the graph potential only depends on the h…
Homological projective duality for the Segre cubic
Thorsten Beckmann, Pieter Belmans
The Segre cubic and Castelnuovo-Richmond quartic are two projectively dual hypersurfaces in , with a long and rich history starting in the 19th century. We will expla…
Polyvector fields for Fano 3-folds
Pieter Belmans, Enrico Fatighenti, Fabio Tanturri
We compute the Hochschild-Kostant-Rosenberg decomposition of the Hochschild cohomology of Fano 3-folds. This is the first step in understanding the non-trivial Gerstenhaber algebra…
Decompositions of moduli spaces of vector bundles and graph potentials
Pieter Belmans, Sergey Galkin, Swarnava Mukhopadhyay
We propose a conjectural semiorthogonal decomposition for the derived category of the moduli space of stable rank 2 bundles with fixed determinant of odd degree, independently form…
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…
Derived categories of the Cayley plane and the coadjoint Grassmannian of type F
Pieter Belmans, Alexander Kuznetsov, Maxim Smirnov
For the derived category of the Cayley plane, which is the cominuscule Grassmannian of Dynkin type , a full Lefschetz exceptional collection was constructed by Faenzi…
Derived categories of flips and cubic hypersurfaces
Pieter Belmans, Lie Fu, Theo Raedschelders
A classical result of Bondal-Orlov states that a standard flip in birational geometry gives rise to a fully faithful functor between derived categories of coherent sheaves. We comp…
Moduli spaces of semiorthogonal decompositions in families
Pieter Belmans, Shinnosuke Okawa, Andrea T. Ricolfi
To a smooth and proper morphism with quasicompact semiseparated target we associate a sheaf in the étale topology, which takes an affine -scheme to the se…
Hochschild cohomology of generalised Grassmannians
Pieter Belmans, Maxim Smirnov
We compute the Hochschild-Kostant-Rosenberg decomposition of the Hochschild cohomology of generalised Grassmannians, i.e. partial flag varieties associated to maximal parabolic sub…
Derived categories of (nested) Hilbert schemes
Pieter Belmans, Andreas Krug
In this paper we provide several results regarding the structure of derived categories of (nested) Hilbert schemes of points. We show that the criteria of Krug-Sosna and Addington…
Automorphisms of Hilbert schemes of points on surfaces
Pieter Belmans, Georg Oberdieck, Jørgen Vold Rennemo
We show that every automorphism of the Hilbert scheme of points on a weak Fano or general type surface is natural, i.e. induced by an automorphism of the surface, unless the su…
Comparison of two constructions of noncommutative surfaces with exceptional collections of length 4
Pieter Belmans, Dennis Presotto, Michel Van den Bergh
Recently the Euler forms on numerical Grothendieck groups of rank 4 whose properties mimick that of the Euler form of a smooth projective surface have been classified. This classif…
Hilbert squares: derived categories and deformations
Pieter Belmans, Lie Fu, Theo Raedschelders
For a smooth projective variety with exceptional structure sheaf, and the Hilbert scheme of two points on , we show that the Fourier-Mukai functor $…
The Hochschild cohomology ring of a global quotient orbifold
Cris Negron, Travis Schedler, Pieter Belmans +1
We study the cup product on the Hochschild cohomology of the stack quotient [X/G] of a smooth quasi-projective variety X by a finite group G. More specifically, we construct a G-eq…
Admissible subcategories in derived categories of moduli of vector bundles on curves
Pieter Belmans, Swarnava Mukhopadhyay
We show that the Poincaré bundle gives a fully faithful embedding from the derived category of a curve of sufficiently high genus into the derived category of its moduli space of b…
Examples violating Golyshev's canonical strip hypotheses
Pieter Belmans, Sergey Galkin, Swarnava Mukhopadhyay
We give the first examples of smooth Fano and Calabi-Yau varieties violating the (narrow) canonical strip hypothesis, which concerns the location of the roots of Hilbert polynomial…