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Inventiones mathematicae, ISSN 0020-9910, 4/2013, Volume 192, Issue 1, pp. 111 - 160
Given a smooth complex threefold X, we define the virtual motive $[\operatorname{Hilb}^{n}(X)]_{\operatorname {vir}}$ of the Hilbert scheme of n points on X.... 
Mathematics, general | Mathematics | 14N35 | 14C05 | 14J30 | MATHEMATICS | GROTHENDIECK RING | POWER-STRUCTURE | PARTITIONS | HILBERT SCHEME | POINTS | Computation
Journal Article
Michigan Mathematical Journal, ISSN 0026-2285, 06/2015, Volume 64, Issue 2, pp. 335 - 347
We prove the algebraicity of the Hilbert functor, the Hilbert stack, the Quot functor, and the stack of coherent sheaves on an algebraic stack X with... 
EXISTENCE | MATHEMATICS | PROOF | ELEMENTARY | EXPLICIT | Mathematics - Algebraic Geometry | 14D23 | 14C05
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 8/2019, Volume 292, Issue 3, pp. 1207 - 1222
Denote by $$\mathcal {H}_{d,g,r}$$ H d , g , r the Hilbert scheme of smooth curves, that is the union of components whose general point corresponds to a smooth... 
Hilbert scheme | 14C20 | Gonality | Mathematics, general | Mathematics | Algebraic curves | Primary 14C05 | Linear series | EXISTENCE | MATHEMATICS | EXPECTED NUMBER
Journal Article
Collectanea Mathematica, ISSN 0010-0757, 1/2018, Volume 69, Issue 1, pp. 39 - 64
Using Macaulay’s correspondence we study the family of Artinian Gorenstein local algebras with fixed symmetric Hilbert function decomposition. As an... 
Geometry | Artinian Gorenstein local algebra | Secondary 14Q15 | Algebra | Cactus rank | Analysis | Mathematics | Applications of Mathematics | Primary 13H10 | 14C05 | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Journal of the Institute of Mathematics of Jussieu, ISSN 1474-7480, 2018, Volume 19, Issue 3, pp. 947 - 964
The motivic Hilbert zeta function of a variety X is the generating function for classes in the Grothendieck ring of varieties of Hilbert schemes of points on... 
14G10 | 14H20 | 2010 Mathematics subject classification | 14C05 | MATHEMATICS | SCHEME | curve singularities | zeta functions | POINTS | Hilbert schemes
Journal Article
Journal de mathématiques pures et appliquées, ISSN 0021-7824, 09/2015, Volume 104, Issue 3, pp. 403 - 435
We consider the construction of refined Chern–Simons torus knot invariants by M. Aganagic and S. Shakirov from the DAHA viewpoint of I. Cherednik. We give a... 
Torus knots | Hilbert scheme | Double affine Hecke algebra | 14F05 | 14C05 | 55A25 | TESLER MATRICES | ELLIPTIC HALL ALGEBRA | MATHEMATICS, APPLIED | COMPACTIFIED JACOBIANS | HECKE ALGEBRAS | AFFINE SPRINGER FIBERS | FINITE-DIMENSIONAL REPRESENTATIONS | RATIONAL CHEREDNIK ALGEBRAS | T-CATALAN NUMBERS | MATHEMATICS | FIXED-POINT VARIETIES | QUOTIENT RING | Algebra
Journal Article
Collectanea Mathematica, ISSN 0010-0757, 1/2017, Volume 68, Issue 1, pp. 101 - 127
The classification of local Artinian Gorenstein algebras is equivalent to the study of orbits of a certain non-reductive group action on a polynomial ring. We... 
Geometry | Algebra | Analysis | Secondary 13N10 | Mathematics | Applications of Mathematics | Primary 13H10 | 14C05 | SYSTEM | MATHEMATICS | FINITE RANK | MATHEMATICS, APPLIED | COMMUTATIVE ALGEBRAS | ISOMORPHISM TYPES
Journal Article
Advances in Geometry, ISSN 1615-715X, 10/2018, Volume 18, Issue 4, pp. 467 - 482
We give linear algebraic and monadic descriptions of the Hilbert scheme of points on the affine space of dimension which naturally extends Nakajima’s... 
Hilbert scheme of points | 14C05 | monads | MATHEMATICS | ALGEBRAS | REPRESENTATIONS | FAMILIES | VARIETIES | Mathematics - Algebraic Geometry
Journal Article
Journal für die reine und angewandte Mathematik (Crelles Journal), ISSN 0075-4102, 10/2017, Volume 2017, Issue 731, pp. 87 - 128
We construct a new twenty-dimensional family of projective eight-dimensional irreducible holomorphic symplectic manifolds: the compactified moduli space of... 
MATHEMATICS | VARIETIES | HILBERT SCHEME | SINGULARITIES | CURVES | SURFACES
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 10/2018, Volume 290, Issue 1, pp. 699 - 710
We show a version of the DT/PT correspondence relating local curve counting invariants, encoding the contribution of a fixed smooth curve in a Calabi–Yau... 
Mathematics, general | Mathematics | Donaldson–Thomas invariants | Hilbert–Chow morphism | 14N35 | 14C05 | THREEFOLDS | MATHEMATICS | Hilbert-Chow morphism | INVARIANTS | Donaldson-Thomas invariants | Mathematics - Algebraic Geometry
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 08/2019, Volume 292, Issue 8, pp. 1777 - 1790
We prove that for every smooth prime Fano 3‐fold V, the Hilbert scheme HilbscV of smooth connected curves on V contains a generically non‐reduced irreducible... 
K3 surface | Primary: 14C05 | obstruction | Hilbert scheme | Fano threefold | Secondary: 14D15 | Hilbert‐flag scheme | 14H10 | Hilbert-flag scheme | MATHEMATICS
Journal Article
Advances in Geometry, ISSN 1615-715X, 07/2019, Volume 19, Issue 3, pp. 353 - 358
We give a new proof of the theorem of Beauville and Voisin about the decomposition of the small diagonal of a K3 surface . Our proof is explicit and works with... 
K3 surface | Chow groups | canonical zero-cycles | K-correspondence | 14C05 | 14C15 | MATHEMATICS | HILBERT SCHEMES | CHOW RINGS | POINTS | Decomposition | Curves
Journal Article
Forum mathematicum, ISSN 1435-5337, 2020, Volume 32, Issue 1, pp. 63 - 78
We study locally Cohen–Macaulay curves of low degree in the Segre threefold and investigate the irreducible and connected components, respectively, of the... 
Locally Cohen–Macaulay curve | moduli space | Hilbert scheme | 14Q05 | pure sheaf | 14H50 | 14C05 | SPACE | MATHEMATICS | MATHEMATICS, APPLIED | Locally Cohen-Macaulay curve | FAMILIES | MODULI
Journal Article
Forum of mathematics. Sigma, ISSN 2050-5094, 2016, Volume 4, pp. 1 - 55
The Hilbert scheme $X^{[3]}$ of length-3 subschemes of a smooth projective variety $X$ is known to be smooth and projective. We investigate whether the... 
Algebraic and Complex Geometry | 14C25 | 14C15 (secondary) | 14C05 (primary) | MATHEMATICS | SURFACE | MATHEMATICS, APPLIED | CHOW RING | CONJECTURES
Journal Article
Mathematische Zeitschrift, ISSN 1432-1823, 2017, Volume 288, Issue 3-4, pp. 803 - 827
Let $$b_{\bullet }$$ b∙ be a sequence of integers $$1 < b_1 \le b_2 \le \cdots \le b_{n-1}$$ 1 Restricted tangent bundles | Normal bundles | Mathematics, general | Rational curves | Mathematics | 14C99 | 14N05 | Primary 14H60 | 14H45 | Secondary 14C05 | MATHEMATICS | RESTRICTED TANGENT BUNDLE
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 6/2016, Volume 182, Issue 1, pp. 73 - 79
Let X be an Abelian threefold. We prove a formula, conjectured by the first author, expressing the Euler characteristic of the generalized Kummer schemes... 
Geometry | Integer partitions | Primary: 14C05 | Donaldson–Thomas invariants | Abelian varieties | Secondary: 14N35 | Kummer schemes | Mathematics
Journal Article
manuscripta mathematica, ISSN 0025-2611, 7/2018, Volume 156, Issue 3, pp. 329 - 340
In this paper, we study local structures of invariant Hilbert schemes with Luna’s étale slice theorem. We prove that in some cases the invariant Hilbert... 
Geometry | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | Mathematics, general | Algebraic Geometry | Mathematics | Number Theory | 14L30 | 14C05
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 2/2015, Volume 279, Issue 1, pp. 139 - 162
Let $$k$$ k be an algebraically closed field and let $$b$$ b and $$n$$ n be integers with $$n\ge 3$$ n ≥ 3 and $$1\le b \le n-1$$ 1 ≤ b ≤ n - 1 . Consider the... 
14G05 | 14G15 | Primary 51N35 | Secondary 14Q10 | Mathematics, general | Mathematics | 14N05 | 14C05 | MATHEMATICS | Mathematics - Algebraic Geometry
Journal Article
Bulletin of the London Mathematical Society, ISSN 0024-6093, 08/2015, Volume 47, Issue 4, pp. 686 - 692
Abstract We prove by explicit example that the compactified jacobian can be nonreduced. The example is a rational space curve of arithmetic genus $4$. This... 
MATHEMATICS | CLASSIFICATION | BUNDLES | MODULI | DIFFEOMORPHISM TYPES | SURFACES | Mathematics - Algebraic Geometry
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 2012, Volume 161, Issue 9, pp. 1797 - 1815
The direct product of two Hilbert schemes of the same surface has natural K-theoly classes given by the alternating Ext-groups between the two ideal sheaves in... 
MATHEMATICS | EQUIVARIANT INTERSECTION THEORY | COHOMOLOGY RING | HILBERT SCHEMES | POINTS | SURFACES | 14D21
Journal Article
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