Advances in Mathematics, ISSN 0001-8708, 11/2018, Volume 338, pp. 601 - 648

We study Hilbert schemes of points on a smooth projective Calabi–Yau 4-fold X. We define DT4 invariants by integrating the Euler class of a tautological vector bundle L[n...

Donaldson–Thomas invariants | Hilbert schemes of points | Solid partitions | Calabi–Yau 4-folds | MATHEMATICS | HILBERT SCHEMES | Donaldson-Thomas invariants | Calabi-Yau 4-folds | POINTS | SHEAVES

Donaldson–Thomas invariants | Hilbert schemes of points | Solid partitions | Calabi–Yau 4-folds | MATHEMATICS | HILBERT SCHEMES | Donaldson-Thomas invariants | Calabi-Yau 4-folds | POINTS | SHEAVES

Journal Article

Memoirs of the American Mathematical Society, ISSN 0065-9266, 05/2012, Volume 217, Issue 1020, pp. 1 - 212

Donaldson-Thomas invariants DT alpha(tau) are integers which 'count' tau-stable coherent sheaves with Chern character a on a Calabi-Yau 3-fold X, where tau denotes Gieseker stability for some ample line bundle on X...

Semistable | Calabi-Yau 3-fold | Vector bundle | Artin stack | Moduli space | Gieseker stability | Donaldson-Thomas invariant | Stability condition | Coherent sheaf | moduli space | BUNDLES | REPRESENTATIONS | DEFORMATION | MODULI SPACES | stability condition | semistable | MATHEMATICS | vector bundle | GROMOV-WITTEN THEORY | COHOMOLOGY | coherent sheaf | CHERN CLASSES | STABILITY CONDITIONS | ABELIAN CATEGORIES | CONFIGURATIONS

Semistable | Calabi-Yau 3-fold | Vector bundle | Artin stack | Moduli space | Gieseker stability | Donaldson-Thomas invariant | Stability condition | Coherent sheaf | moduli space | BUNDLES | REPRESENTATIONS | DEFORMATION | MODULI SPACES | stability condition | semistable | MATHEMATICS | vector bundle | GROMOV-WITTEN THEORY | COHOMOLOGY | coherent sheaf | CHERN CLASSES | STABILITY CONDITIONS | ABELIAN CATEGORIES | CONFIGURATIONS

Journal Article

Quarterly Journal of Mathematics, ISSN 0033-5606, 09/2016, Volume 67, Issue 3, pp. 365 - 386

.... The action of C* on the fibres of X induces an action on the moduli space and the stable pair invariants of X are defined by the virtual localization formula...

GROMOV | MATHEMATICS | TORIC 3-FOLDS | DONALDSON-THOMAS THEORY | CURVES | POINCARE INVARIANTS

GROMOV | MATHEMATICS | TORIC 3-FOLDS | DONALDSON-THOMAS THEORY | CURVES | POINCARE INVARIANTS

Journal Article

Advances in Mathematics, ISSN 0001-8708, 11/2018, Volume 338, pp. 41 - 92

In analogy with the Gopakumar–Vafa conjecture on CY 3-folds, Klemm and Pandharipande defined GV type invariants on Calabi...

Donaldson–Thomas invariants | Gopakumar–Vafa invariants | Calabi–Yau 4-folds | ENUMERATIVE GEOMETRY | MATHEMATICS | Donaldson-Thomas invariants | K3 SURFACES | CYCLES | Calabi-Yau 4-folds | Gopakumar-Vafa invariants | DONALDSON-THOMAS THEORY | CURVES

Donaldson–Thomas invariants | Gopakumar–Vafa invariants | Calabi–Yau 4-folds | ENUMERATIVE GEOMETRY | MATHEMATICS | Donaldson-Thomas invariants | K3 SURFACES | CYCLES | Calabi-Yau 4-folds | Gopakumar-Vafa invariants | DONALDSON-THOMAS THEORY | CURVES

Journal Article

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Donaldson–Thomas invariants of 2-dimensional sheaves inside threefolds and modular forms

Advances in Mathematics, ISSN 0001-8708, 02/2018, Volume 326, pp. 79 - 107

Motivated by the S-duality conjecture, we study the Donaldson–Thomas invariants of the 2-dimensional Gieseker stable sheaves on a threefold...

Donaldson–Thomas invariants | K3 fibration | Noether–Lefschetz numbers | S-duality | Hilbert scheme | Modularity | QUOT-SCHEMES | BUNDLES | STACKS | CURVES | MATHEMATICS | CALABI-YAU 3-FOLDS | Donaldson-Thomas invariants | Noether-Lefschetz numbers | K3 SURFACES | POINTS

Donaldson–Thomas invariants | K3 fibration | Noether–Lefschetz numbers | S-duality | Hilbert scheme | Modularity | QUOT-SCHEMES | BUNDLES | STACKS | CURVES | MATHEMATICS | CALABI-YAU 3-FOLDS | Donaldson-Thomas invariants | Noether-Lefschetz numbers | K3 SURFACES | POINTS

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 6/2014, Volume 328, Issue 3, pp. 903 - 954

A refinement of the stable pair invariants of Pandharipande and Thomas for non-compact Calabi...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | GAUGE-THEORY | DONALDSON-THOMAS INVARIANTS | GOPAKUMAR-VAFA | PHYSICS, MATHEMATICAL | GROMOV-WITTEN | VERTEX

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | GAUGE-THEORY | DONALDSON-THOMAS INVARIANTS | GOPAKUMAR-VAFA | PHYSICS, MATHEMATICAL | GROMOV-WITTEN | VERTEX

Journal Article

Compositio mathematica, ISSN 0010-437X, 08/2015, Volume 151, Issue 8, pp. 1543 - 1567

.... This leads naturally to a definition of a class of putative $q$-deformed Gromov–Witten invariants. We prove that this coincides with another natural...

wall-crossing | Gromov-Witten invariants | tropical counts | MATHEMATICS | REFINED GW/KRONECKER CORRESPONDENCE | NUMBERS | DONALDSON-THOMAS INVARIANTS | CURVES | QUIVER MODULI | SURFACES | Mathematics | Blocking | Representations | Formalism | Invariants | Counting | Algebraic Geometry

wall-crossing | Gromov-Witten invariants | tropical counts | MATHEMATICS | REFINED GW/KRONECKER CORRESPONDENCE | NUMBERS | DONALDSON-THOMAS INVARIANTS | CURVES | QUIVER MODULI | SURFACES | Mathematics | Blocking | Representations | Formalism | Invariants | Counting | Algebraic Geometry

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 11/2014, Volume 331, Issue 3, pp. 1029 - 1039

We show that the refined Donaldson–Thomas invariants of $${\mathbb{C}^3}$$ C 3 , suitably normalized, have a Gaussian distribution as limit law...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | PHYSICS, MATHEMATICAL | DONALDSON-THOMAS INVARIANTS | Analysis | Gaussian processes

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | PHYSICS, MATHEMATICAL | DONALDSON-THOMAS INVARIANTS | Analysis | Gaussian processes

Journal Article

Algebra and Number Theory, ISSN 1937-0652, 2017, Volume 11, Issue 6, pp. 1243 - 1286

We calculate the motivic Donaldson-Thomas invariants for (-2)-curves arising from 3-fold flopping contractions in the minimal model program...

Donaldson-Thomas theory | Motivic invariants | Minus two curves | MATHEMATICS | CONIFOLD | motivic invariants | CALABI-YAU 3-FOLDS | STABILITY CONDITIONS | minus two curves | ABELIAN CATEGORIES | HALL ALGEBRAS | CONFIGURATIONS | ARTIN STACKS | CONJECTURE | Mathematics - Algebraic Geometry

Donaldson-Thomas theory | Motivic invariants | Minus two curves | MATHEMATICS | CONIFOLD | motivic invariants | CALABI-YAU 3-FOLDS | STABILITY CONDITIONS | minus two curves | ABELIAN CATEGORIES | HALL ALGEBRAS | CONFIGURATIONS | ARTIN STACKS | CONJECTURE | Mathematics - Algebraic Geometry

Journal Article

Annales Henri Poincaré, ISSN 1424-0637, 1/2018, Volume 19, Issue 1, pp. 1 - 70

.... Framed BPS states can be thought of as BPS particles bound to the defect. We identify the framed BPS degeneracies with certain enumerative invariants associated with the moduli spaces of stable quiver representations...

Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Quantum Physics | Dynamical Systems and Ergodic Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | STATES | PHYSICS, MULTIDISCIPLINARY | COHOMOLOGICAL GAUGE-THEORY | SPECTRAL NETWORKS | DUALITY | DONALDSON-THOMAS INVARIANTS | PHYSICS, MATHEMATICAL | PHYSICS, PARTICLES & FIELDS | Analysis | Numerical analysis

Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Quantum Physics | Dynamical Systems and Ergodic Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | STATES | PHYSICS, MULTIDISCIPLINARY | COHOMOLOGICAL GAUGE-THEORY | SPECTRAL NETWORKS | DUALITY | DONALDSON-THOMAS INVARIANTS | PHYSICS, MATHEMATICAL | PHYSICS, PARTICLES & FIELDS | Analysis | Numerical analysis

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 03/2016, Volume 368, Issue 3, pp. 1583 - 1619

We construct curve counting invariants for a Calabi-Yau threefold Y \pi :Y \to X \pi :Y\to Y is a crepant resolution of X...

THREEFOLDS | MATHEMATICS | STABLE PAIRS | CALABI-YAU 3-FOLDS | MCKAY CORRESPONDENCE | DONALDSON-THOMAS INVARIANTS | STABILITY CONDITIONS | ABELIAN CATEGORIES | HALL ALGEBRAS | CONFIGURATIONS | SCHEMES

THREEFOLDS | MATHEMATICS | STABLE PAIRS | CALABI-YAU 3-FOLDS | MCKAY CORRESPONDENCE | DONALDSON-THOMAS INVARIANTS | STABILITY CONDITIONS | ABELIAN CATEGORIES | HALL ALGEBRAS | CONFIGURATIONS | SCHEMES

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 4/2016, Volume 282, Issue 3, pp. 867 - 887

We use the degeneration formula and the absolute/relative correspondence tostudy the change of stable pair invariants of threefold under blow-ups and obtain some closed blow-up formulae, which imply...

BPS state count | 14N35 | Stable pair invariant | Absolute/relative correspondence | Mathematics, general | Mathematics | Degeneration formula | GW/DT/P correspondence | Blow-up | FACTORIZATION | DONALDSON-THOMAS THEORY | FORMULA | CURVES | DEGENERATION | MATHEMATICS | TORIC 3-FOLDS | DESCENDANTS | MANIFOLDS | GROMOV-WITTEN INVARIANTS | SURFACES

BPS state count | 14N35 | Stable pair invariant | Absolute/relative correspondence | Mathematics, general | Mathematics | Degeneration formula | GW/DT/P correspondence | Blow-up | FACTORIZATION | DONALDSON-THOMAS THEORY | FORMULA | CURVES | DEGENERATION | MATHEMATICS | TORIC 3-FOLDS | DESCENDANTS | MANIFOLDS | GROMOV-WITTEN INVARIANTS | SURFACES

Journal Article

Advances in Mathematics, ISSN 0001-8708, 2010, Volume 223, Issue 5, pp. 1521 - 1544

.... Under certain consistency conditions on a brane tiling, we prove a formula for the Donaldson–Thomas type invariants of the moduli space of framed cyclic modules over the corresponding quiver potential algebra...

Brane tiling | Donaldson–Thomas invariant | Hilbert scheme | Quiver potential algebra | Donaldson-Thomas invariant | MATHEMATICS

Brane tiling | Donaldson–Thomas invariant | Hilbert scheme | Quiver potential algebra | Donaldson-Thomas invariant | MATHEMATICS

Journal Article

Journal of Noncommutative Geometry, ISSN 1661-6952, 2017, Volume 11, Issue 3, pp. 1115 - 1139

This paper is motivated by the question of how motivic Donaldson-Thomas invariants behave in families...

Motivic vanishing cycle | Dimensional reduction | Donaldson-Thomas theory | Quiver representation | Calabi-Yau algebra | MATHEMATICS, APPLIED | SPACES | DIMENSION-3 | FIELD | VARIETIES | PHYSICS, MATHEMATICAL | quiver representation | MATHEMATICS | ALGEBRAS | CONIFOLD | dimensional reduction | motivic vanishing cycle | GEOMETRY

Motivic vanishing cycle | Dimensional reduction | Donaldson-Thomas theory | Quiver representation | Calabi-Yau algebra | MATHEMATICS, APPLIED | SPACES | DIMENSION-3 | FIELD | VARIETIES | PHYSICS, MATHEMATICAL | quiver representation | MATHEMATICS | ALGEBRAS | CONIFOLD | dimensional reduction | motivic vanishing cycle | GEOMETRY

Journal Article

Confluentes Mathematici, ISSN 1793-7442, 2017, Volume 9, Issue 2, pp. 71 - 99

Confluentes Mathematici 9 (2017) 2, 71-99 In this note we review some of the uses of framed quivers to study BPS invariants of Donaldson-Thomas type...

Defects in quantum field theory | Donaldson-Thomas theory | Quivers and representation theory | BPS invariants

Defects in quantum field theory | Donaldson-Thomas theory | Quivers and representation theory | BPS invariants

Journal Article

Algebra and Number Theory, ISSN 1937-0652, 2018, Volume 12, Issue 5, pp. 1001 - 1025

.... For symmetric quivers, this leads to an identification of their quantized Donaldson-Thomas invariants with the Chow-Betti numbers of moduli spaces.

Cohomological Hall algebra | Donaldson-Thomas invariants | Quiver moduli | MATHEMATICS | MODULES | COHOMOLOGY | quiver moduli | QUANTUM GROUPS | RINGS | COHA | cohomological Hall algebra

Cohomological Hall algebra | Donaldson-Thomas invariants | Quiver moduli | MATHEMATICS | MODULES | COHOMOLOGY | quiver moduli | QUANTUM GROUPS | RINGS | COHA | cohomological Hall algebra

Journal Article

Journal of Algebra, ISSN 0021-8693, 02/2014, Volume 400, pp. 299 - 314

... A[−1]. On that conditions the refined Donaldson–Thomas invariant associated to (Q,W) is independent of the chosen central charge.

Quivers with potential | Donaldson–Thomas invariants | Bridgeland stability conditions | Donaldson-Thomas invariants | MATHEMATICS | STABILITY CONDITIONS | Bridge land stability conditions | QUIVERS | Algebra

Quivers with potential | Donaldson–Thomas invariants | Bridgeland stability conditions | Donaldson-Thomas invariants | MATHEMATICS | STABILITY CONDITIONS | Bridge land stability conditions | QUIVERS | Algebra

Journal Article

PURE AND APPLIED MATHEMATICS QUARTERLY, ISSN 1558-8599, 2017, Volume 13, Issue 3, pp. 517 - 562

We propose a definition of Vafa-Witten invariants counting semistable Higgs pairs on a polarised surface...

MATHEMATICS | MATHEMATICS, APPLIED | YANG-MILLS | DONALDSON-THOMAS INVARIANTS | ABELIAN CATEGORIES | CONFIGURATIONS | SHEAVES | MODULI | ARTIN STACKS

MATHEMATICS | MATHEMATICS, APPLIED | YANG-MILLS | DONALDSON-THOMAS INVARIANTS | ABELIAN CATEGORIES | CONFIGURATIONS | SHEAVES | MODULI | ARTIN STACKS

Journal Article

Compositio mathematica, ISSN 0010-437X, 03/2013, Volume 149, Issue 3, pp. 495 - 504

We derive some combinatorial consequences from the positivity of Donaldson–Thomas invariants for symmetric quivers conjectured by Kontsevich and Soibelman and proved recently by Efimov...

Kac conjecture | Donaldson-Thomas invariants | MATHEMATICS | COHOMOLOGICAL HALL ALGEBRA | REPRESENTATIONS | QUIVERS | Combinatorics | Theorems | Algebra | Invariants | Combinatorial analysis

Kac conjecture | Donaldson-Thomas invariants | MATHEMATICS | COHOMOLOGICAL HALL ALGEBRA | REPRESENTATIONS | QUIVERS | Combinatorics | Theorems | Algebra | Invariants | Combinatorial analysis

Journal Article

Geometry and Topology, ISSN 1465-3060, 10/2015, Volume 19, Issue 5, pp. 2535 - 2555

We compute the motivic Donaldson-Thomas invariants of the one-loop quiver, with an arbitrary potential...

Motivic donaldson–thomas theory | Vanishing cycles | Quivers | MATHEMATICS | CONFIGURATIONS | ABELIAN CATEGORIES

Motivic donaldson–thomas theory | Vanishing cycles | Quivers | MATHEMATICS | CONFIGURATIONS | ABELIAN CATEGORIES

Journal Article

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