Orbifolds and finite group representations by Li Chiang, Shi-Shyr Roan

“…For n=4, the structure of Hilbert scheme of group orbits and crepant resolutions of Ar(4)-singularity are obtained. …”
Get full text

Integral cohomology of quotients via toric geometry by Grégoire Menet

“…As an application, we compute the Beauville--Bogomolov form of $X/G$ when $X$ is a Hilbert scheme of points on a K3 surface and $G$ a symplectic automorphism group of orders 5 or 7.…”
Get full text

Combinatorial Reid's recipe for consistent dimer models by Alastair Craw, Liana Heuberger, Jesus Tapia Amador

“…Reid's recipe for a finite abelian subgroup $G\subset \text{SL}(3,\mathbb{C})$ is a combinatorial procedure that marks the toric fan of the $G$-Hilbert scheme with irreducible representations of $G$. …”
Get full text

Superconformal quantum mechanics and growth of sheaf cohomology by Nick Dorey, Boan Zhao

“…In the special case of the Hilbert scheme of K points on ℂ2, we obtain a rigorous estimate for the exponential growth of the index degeneracies of BPS states as K → ∞. …”
Get full text

Quot schemes for Kleinian orbifolds by Craw, A, Gammelgaard, S, Gyenge, Á, Szendrői, B

“…Our results generalise our previous work on the Hilbert scheme of points on $\mathbb{C}^2/\Gamma$; we present arguments that completely bypass the ADE classification.…”

The operator rings of topological symmetric orbifolds and their large N limit by Sujay K. Ashok, Jan Troost

“…Our analysis applies to all second quantized Frobenius algebras, a large class of algebras that includes the cohomology ring of the Hilbert scheme of points on K3 among many others. We point out interesting open questions that our results raise.…”
Get full text

The Chow of S (inverted right perpendicular n inverted left perpendicular) and the universal subscheme by Negut, Andrei

“…We prove that any element in the Chow ring of the Hilbert scheme Hilbn of n points on a smooth surface S is a universal class, i.e. the push-forward of a polynomial in the Chern classes of the universal subschemes on Hilb[subscript n] x S[superscript K] for some k ∈N, with coefficients pulled back from the Chow of S[superscript K].…”
Get full text

THE MOTIVE OF THE HILBERT CUBE $X^{[3]}$ by MINGMIN SHEN, CHARLES VIAL

“…The Hilbert scheme $X^{[3]}$ of length-3 subschemes of a smooth projective variety $X$ is known to be smooth and projective. …”
Get full text

S[subscript n]-equivariant sheaves and Koszul cohomology by Yang, David H.

“…Purpose: We give a new interpretation of Koszul cohomology, which is equivalent under the Bridgeland-King-Reid equivalence to Voisin's Hilbert scheme interpretation in dimensions 1 and 2 but is different in higher dimensions. …”
Get full text

The topological symmetric orbifold by Songyuan Li, Jan Troost

“…Indeed, we propose a concrete mathematical incarnation of the proof, relating Gromow-Witten theory in the bulk to the cohomology of the Hilbert scheme on the boundary.…”
Get full text

On product identities and the Chow rings of holomorphic symplectic varieties by Barros, Ignacio, Flapan, Laure, Marian, Alina, Silversmith, Rob

“…We prove the proposed identities when $${\mathsf M}$$ M is the Hilbert scheme of points on a K3 surface.…”
Get full text

Infinitesimal change of stable basis by Gorsky, Eugene, Negut, Andrei

“…The purpose of this note is to study the Maulik–Okounkov K-theoretic stable basis for the Hilbert scheme of points on the plane, which depends on a “slope” m∈R. …”
Get full text
Get full text

A Topological View of Reed–Solomon Codes by Alberto Besana, Cristina Martínez

“…We characterized the coefficients that appear in the decompostion of an irreducible representation of the special linear group in terms of Gromov–Witten invariants of the Hilbert scheme of points in the plane. In addition, we classified all the algebraic codes defined over the normal rational curve, thereby providing an algorithm to compute a set of generators of the ideal associated with any algebraic code constructed on the rational normal curve (NRC) over an extension <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="double-struck">F</mi><msup><mi>q</mi><mi>n</mi></msup></msub></semantics></math></inline-formula> of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="double-struck">F</mi><mi>q</mi></msub></semantics></math></inline-formula>.…”
Get full text

The geometry of some moduli schemes arising in enumerative geometry by Carlucci, A

“…The main technical obstacle is that, while stability for the Hilbert scheme (leading to Donaldson-Thomas invariants) translates to a simple algebraic condition, stability of PT-pairs involves a case-by-case analysis to obtain suitable algebraic conditions on the corresponding quiver representations.…”

Wall-crossing and orientations for invariants counting coherent sheaves on CY fourfolds by Bojko, A

“…We begin, by addressing the conjecture of Cao–Kool , which expresses the virtual integrals of a tautological line bundle L^[n] on the Hilbert scheme of points Hilbⁿ (X) in terms of the MacMahon function. …”

Flags of sheaves, quivers and symmetric polynomials by Giulio Bonelli, Nadir Fasola, Alessandro Tanzini

“…We study a quiver description of the nested Hilbert scheme of points on the affine plane and its higher rank generalization – that is, the moduli space of flags of framed torsion-free sheaves on the projective plane. …”
Get full text

Finite dimensional representations of sympletic reflection algebras for wreath products by Montarani, Silvia

Get full text

On some computations of refined Donaldson-Thomas invariants by Cazzaniga, A

“…</p> <p>In Chapter 2 we compute the generating series of refined DT invariants for the moduli space 𝑀_n,r of higher rank framed sheaves on ℙ³, generalizing the result of [BBS] for the Hilbert scheme of <em>n</em> points on ℂ³. …”

Categorical and K-theoretic Donaldson–Thomas theory of $\mathbb {C}^3$ (part II) by Tudor Pădurariu, Yukinobu Toda

“…Quasi-BPS categories appear as summands in semiorthogonal decompositions of DT categories for Hilbert schemes of points in the three-dimensional affine space and in the categorical Hall algebra of the two-dimensional affine space. …”
Get full text

Autoduality of the Hitchin system and the geometric Langlands programme by Groechenig, M

“…Furthermore, the Hilbert schemes of points of these surfaces are equivalent to moduli spaces of parabolic Higgs bundles, respectively local systems (Theorem 5.3.1). …”