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Artykuły w czasopismach na temat „Donaldson-Thomas invariant”

Autor: Grafiati

Data publikacji: 2 czerwca 2025

Data aktualizacji: 31 lipca 2025

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1

Meinhardt, Sven, and Markus Reineke. "Donaldson–Thomas invariants versus intersection cohomology of quiver moduli." Journal für die reine und angewandte Mathematik (Crelles Journal) 2019, no. 754 (2019): 143–78. http://dx.doi.org/10.1515/crelle-2017-0010.

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Abstract The main result of this paper is the statement that the Hodge theoretic Donaldson–Thomas invariant for a quiver with zero potential and a generic stability condition agrees with the compactly supported intersection cohomology of the closure of the stable locus inside the associated coarse moduli space of semistable quiver representations. In fact, we prove an even stronger result relating the Donaldson–Thomas “function” to the intersection complex. The proof of our main result relies on a relative version of the integrality conjecture in Donaldson–Thomas theory. This will be the topic

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2

Oberdieck, Georg, Dulip Piyaratne, and Yukinobu Toda. "Donaldson–Thomas invariants of abelian threefolds and Bridgeland stability conditions." Journal of Algebraic Geometry 31, no. 1 (2021): 13–73. http://dx.doi.org/10.1090/jag/788.

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We study the reduced Donaldson–Thomas theory of abelian threefolds using Bridgeland stability conditions. The main result is the invariance of the reduced Donaldson–Thomas invariants under all derived autoequivalences, up to explicitly given wall-crossing terms. We also present a numerical criterion for the absence of walls in terms of a discriminant function. For principally polarized abelian threefolds of Picard rank one, the wall-crossing contributions are discussed in detail. The discussion yields evidence for a conjectural formula for curve counting invariants by Bryan, Pandharipande, Yin

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3

Joyce, Dominic. "Generalized Donaldson-Thomas invariants." Surveys in Differential Geometry 16, no. 1 (2011): 125–60. http://dx.doi.org/10.4310/sdg.2011.v16.n1.a4.

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4

Efimov, Alexander I. "Cohomological Hall algebra of a symmetric quiver." Compositio Mathematica 148, no. 4 (2012): 1133–46. http://dx.doi.org/10.1112/s0010437x12000152.

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AbstractIn [M. Kontsevich and Y. Soibelman, Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson–Thomas invariants, Preprint (2011), arXiv:1006.2706v2[math.AG]], the authors, in particular, associate to each finite quiver Q with a set of vertices I the so-called cohomological Hall algebra ℋ, which is ℤI≥0-graded. Its graded component ℋγ is defined as cohomology of the Artin moduli stack of representations with dimension vector γ. The product comes from natural correspondences which parameterize extensions of representations. In the case of a symmetric quiver, one can

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5

Behrend, Kai, and Jim Bryan. "Super-rigid Donaldson-Thomas Invariants." Mathematical Research Letters 14, no. 4 (2007): 559–71. http://dx.doi.org/10.4310/mrl.2007.v14.n4.a2.

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6

Cirafici, M., A. Sinkovics, and R. J. Szabo. "Instantons and Donaldson-Thomas invariants." Fortschritte der Physik 56, no. 7-9 (2008): 849–55. http://dx.doi.org/10.1002/prop.200810544.

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7

Koshkin, Sergiy. "Quantum Barnes Function as the Partition Function of the Resolved Conifold." International Journal of Mathematics and Mathematical Sciences 2008 (2008): 1–47. http://dx.doi.org/10.1155/2008/438648.

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We give a short new proof of largeNduality between the Chern-Simons invariants of the 3-sphere and the Gromov-Witten/Donaldson-Thomas invariants of the resolved conifold. Our strategy applies to more general situations, and it is to interpret the Gromov-Witten, the Donaldson-Thomas, and the Chern-Simons invariants as different characterizations of the same holomorphic function. For the resolved conifold, this function turns out to be the quantum Barnes function, a naturalq-deformation of the classical one that in its turn generalizes the Euler gamma function. Our reasoning is based on a new fo

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8

Behrend, Kai, Jim Bryan, and Balázs Szendrői. "Motivic degree zero Donaldson–Thomas invariants." Inventiones mathematicae 192, no. 1 (2012): 111–60. http://dx.doi.org/10.1007/s00222-012-0408-1.

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9

Ricolfi, Andrea T. "Local Contributions to Donaldson–Thomas Invariants." International Mathematics Research Notices 2018, no. 19 (2017): 5995–6025. http://dx.doi.org/10.1093/imrn/rnx046.

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10

Engenhorst, Magnus. "Tilting and refined Donaldson–Thomas invariants." Journal of Algebra 400 (February 2014): 299–314. http://dx.doi.org/10.1016/j.jalgebra.2013.12.004.

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11

Li, Jun. "Zero dimensional Donaldson–Thomas invariants of threefolds." Geometry & Topology 10, no. 4 (2006): 2117–71. http://dx.doi.org/10.2140/gt.2006.10.2117.

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12

Behrend, Kai. "Donaldson-Thomas type invariants via microlocal geometry." Annals of Mathematics 170, no. 3 (2009): 1307–38. http://dx.doi.org/10.4007/annals.2009.170.1307.

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13

Joyce, Dominic, and Yinan Song. "A theory of generalized Donaldson–Thomas invariants." Memoirs of the American Mathematical Society 217, no. 1020 (2012): 0. http://dx.doi.org/10.1090/s0065-9266-2011-00630-1.

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14

Ke, Hua-Zhong. "A flop formula for Donaldson–Thomas invariants." Mathematical Research Letters 26, no. 1 (2019): 203–30. http://dx.doi.org/10.4310/mrl.2019.v26.n1.a10.

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15

Argüz, Hülya, and Pierrick Bousseau. "The flow tree formula for Donaldson–Thomas invariants of quivers with potentials." Compositio Mathematica 158, no. 12 (2022): 2206–49. http://dx.doi.org/10.1112/s0010437x22007801.

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We prove the flow tree formula conjectured by Alexandrov and Pioline, which computes Donaldson–Thomas invariants of quivers with potentials in terms of a smaller set of attractor invariants. This result is obtained as a particular case of a more general flow tree formula reconstructing a consistent scattering diagram from its initial walls.

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16

Leigh, Oliver. "UNWEIGHTED DONALDSON–THOMAS THEORY OF THE BANANA 3-FOLD WITH SECTION CLASSES." Quarterly Journal of Mathematics 71, no. 3 (2020): 867–942. http://dx.doi.org/10.1093/qmathj/haaa007.

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Abstract We further the study of the Donaldson–Thomas theory of the banana 3-folds which were recently discovered and studied by Bryan [3]. These are smooth proper Calabi–Yau 3-folds which are fibred by Abelian surfaces such that the singular locus of a singular fibre is a non-normal toric curve known as a ‘banana configuration’. In [3], the Donaldson–Thomas partition function for the rank 3 sub-lattice generated by the banana configurations is calculated. In this article, we provide calculations with a view towards the rank 4 sub-lattice generated by a section and the banana configurations. W

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17

Mozgovoy, Sergey. "Motivic Donaldson–Thomas invariants and the Kac conjecture." Compositio Mathematica 149, no. 3 (2013): 495–504. http://dx.doi.org/10.1112/s0010437x13007148.

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AbstractWe derive some combinatorial consequences from the positivity of Donaldson–Thomas invariants for symmetric quivers conjectured by Kontsevich and Soibelman and proved recently by Efimov. These results are used to prove the Kac conjecture for quivers having at least one loop at every vertex.

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18

Kinjo, Tasuki. "Dimensional reduction in cohomological Donaldson–Thomas theory." Compositio Mathematica 158, no. 1 (2022): 123–67. http://dx.doi.org/10.1112/s0010437x21007740.

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For oriented $-1$-shifted symplectic derived Artin stacks, Ben-Bassat, Brav, Bussi and Joyce introduced certain perverse sheaves on them which can be regarded as sheaf-theoretic categorifications of the Donaldson–Thomas invariants. In this paper, we prove that the hypercohomology of the above perverse sheaf on the $-1$-shifted cotangent stack over a quasi-smooth derived Artin stack is isomorphic to the Borel–Moore homology of the base stack up to a certain shift of degree. This is a global version of the dimensional reduction theorem due to Davison. We give two applications of our main theorem

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19

Reineke, Markus. "Poisson automorphisms and quiver moduli." Journal of the Institute of Mathematics of Jussieu 9, no. 3 (2009): 653–67. http://dx.doi.org/10.1017/s1474748009000176.

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AbstractA factorization formula for certain automorphisms of a Poisson algebra associated with a quiver is proved, which involves framed versions of moduli spaces of quiver representations. This factorization formula is related to wall-crossing formulae for Donaldson–Thomas type invariants of Kontsevich and Soibelman.

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20

Morrison, Andrew, and Kentaro Nagao. "Motivic Donaldson–Thomas invariants of small crepant resolutions." Algebra & Number Theory 9, no. 4 (2015): 767–813. http://dx.doi.org/10.2140/ant.2015.9.767.

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21

Davison, Ben, and Sven Meinhardt. "The motivic Donaldson–Thomas invariants of (−2)-curves." Algebra & Number Theory 11, no. 6 (2017): 1243–86. http://dx.doi.org/10.2140/ant.2017.11.1243.

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22

Szendrői, Balázs. "Non-commutative Donaldson–Thomas invariants and the conifold." Geometry & Topology 12, no. 2 (2008): 1171–202. http://dx.doi.org/10.2140/gt.2008.12.1171.

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23

Cazzaniga, Alberto, Andrew Morrison, Brent Pym, and Balázs Szendrői. "Motivic Donaldson–Thomas invariants of some quantized threefolds." Journal of Noncommutative Geometry 11, no. 3 (2017): 1115–39. http://dx.doi.org/10.4171/jncg/11-3-10.

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24

Franzen, Hans, and Matthew B. Young. "Cohomological orientifold Donaldson–Thomas invariants as Chow groups." Selecta Mathematica 24, no. 3 (2018): 2035–61. http://dx.doi.org/10.1007/s00029-018-0415-1.

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25

Hu, Jianxun, and Wei-Ping Li. "The Donaldson-Thomas invariants under blowups and flops." Journal of Differential Geometry 90, no. 3 (2012): 391–411. http://dx.doi.org/10.4310/jdg/1335273389.

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26

Hu, Jianxun. "Local Donaldson–Thomas invariants of blowups of surfaces." Asian Journal of Mathematics 21, no. 1 (2017): 175–84. http://dx.doi.org/10.4310/ajm.2017.v21.n1.a5.

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27

Gulbrandsen, Martin G. "Donaldson–Thomas invariants for complexes on abelian threefolds." Mathematische Zeitschrift 273, no. 1-2 (2012): 219–36. http://dx.doi.org/10.1007/s00209-012-1002-3.

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28

Reineke, Markus. "Cohomology of quiver moduli, functional equations, and integrality of Donaldson–Thomas type invariants." Compositio Mathematica 147, no. 3 (2011): 943–64. http://dx.doi.org/10.1112/s0010437x1000521x.

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AbstractA system of functional equations relating the Euler characteristics of moduli spaces of stable representations of quivers and the Euler characteristics of (Hilbert-scheme-type) framed versions of quiver moduli is derived. This is applied to wall-crossing formulas for the Donaldson–Thomas type invariants of M. Kontsevich and Y. Soibelman, in particular confirming their integrality.

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29

Gholampour, Amin, and Hsian-Hua Tseng. "On Donaldson-Thomas invariants of threefold stacks and gerbes." Proceedings of the American Mathematical Society 141, no. 1 (2012): 191–203. http://dx.doi.org/10.1090/s0002-9939-2012-11346-2.

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30

Calabrese, John. "On the crepant resolution conjecture for Donaldson-Thomas invariants." Journal of Algebraic Geometry 25, no. 1 (2015): 1–18. http://dx.doi.org/10.1090/jag/660.

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31

Toda, Yukinobu. "Generalized Donaldson–Thomas invariants on the local projective plane." Journal of Differential Geometry 106, no. 2 (2017): 341–69. http://dx.doi.org/10.4310/jdg/1497405629.

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32

Cirafici, Michele. "Defects in cohomological gauge theory and Donaldson–Thomas invariants." Advances in Theoretical and Mathematical Physics 20, no. 5 (2016): 945–1006. http://dx.doi.org/10.4310/atmp.2016.v20.n5.a1.

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33

Li, Wei-Ping, and Zhenbo Qin. "Donaldson–Thomas invariants of certain Calabi–Yau 3-folds." Communications in Analysis and Geometry 21, no. 3 (2013): 541–78. http://dx.doi.org/10.4310/cag.2013.v21.n3.a4.

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34

Toda, Yukinobu. "On a computation of rank two Donaldson–Thomas invariants." Communications in Number Theory and Physics 4, no. 1 (2010): 49–102. http://dx.doi.org/10.4310/cntp.2010.v4.n1.a2.

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35

Diaconescu, Duiliu-Emanuel, Zheng Hua, and Yan Soibelman. "HOMFLY polynomials, stable pairs and motivic Donaldson–Thomas invariants." Communications in Number Theory and Physics 6, no. 3 (2012): 517–600. http://dx.doi.org/10.4310/cntp.2012.v6.n3.a1.

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36

Young, Matthew B. "Self-dual quiver moduli and orientifold Donaldson-Thomas invariants." Communications in Number Theory and Physics 9, no. 3 (2015): 437–75. http://dx.doi.org/10.4310/cntp.2015.v9.n3.a1.

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37

Jiang, Yunfeng. "Donaldson–Thomas invariants of Calabi–Yau orbifolds under flops." Illinois Journal of Mathematics 62, no. 1-4 (2018): 61–97. http://dx.doi.org/10.1215/ijm/1552442657.

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38

Gholampour, Amin, and Artan Sheshmani. "Donaldson–Thomas invariants, linear systems and punctual Hilbert schemes." Mathematical Research Letters 29, no. 4 (2022): 1049–64. http://dx.doi.org/10.4310/mrl.2022.v29.n4.a6.

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39

Espreafico, Felipe, and Johannes Walcher. "On motivic and arithmetic refinements of Donaldson-Thomas invariants." Communications in Number Theory and Physics 18, no. 1 (2024): 153–79. http://dx.doi.org/10.4310/cntp.2024.v18.n1.a3.

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40

Bayer, Arend, Martí Lahoz, Emanuele Macrì, Howard Nuer, Alexander Perry, and Paolo Stellari. "Stability conditions in families." Publications mathématiques de l'IHÉS 133, no. 1 (2021): 157–325. http://dx.doi.org/10.1007/s10240-021-00124-6.

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AbstractWe develop a theory of Bridgeland stability conditions and moduli spaces of semistable objects for a family of varieties. Our approach is based on and generalizes previous work by Abramovich–Polishchuk, Kuznetsov, Lieblich, and Piyaratne–Toda. Our notion includes openness of stability, semistable reduction, a support property uniformly across the family, and boundedness of semistable objects. We show that such a structure exists whenever stability conditions are known to exist on the fibers.Our main application is the generalization of Mukai’s theory for moduli spaces of semistable she

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41

LI, WEI-PING, and ZHENBO QIN. "STABLE RANK-2 BUNDLES ON CALABI–YAU MANIFOLDS." International Journal of Mathematics 14, no. 10 (2003): 1097–120. http://dx.doi.org/10.1142/s0129167x03002150.

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In this paper, we apply the technique of chamber structures of stability polarizations to construct the full moduli space of rank-2 stable sheaves with certain Chern classes on Calabi–Yau manifolds which are anti-canonical divisor of ℙ1×ℙn or a double cover of ℙ1×ℙn. These moduli spaces are isomorphic to projective spaces. As an application, we compute the holomorphic Casson invariants defined by Donaldson and Thomas.

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42

Le Bruyn, Lieven. "Brauer–Severi motives and Donaldson–Thomas invariants of quantized threefolds." Journal of Noncommutative Geometry 12, no. 2 (2018): 671–92. http://dx.doi.org/10.4171/jncg/288.

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43

Oberdieck, Georg, and Junliang Shen. "Reduced Donaldson-Thomas invariants and the ring of dual numbers." Proceedings of the London Mathematical Society 118, no. 1 (2018): 191–220. http://dx.doi.org/10.1112/plms.12178.

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44

Cao, Yalong, and Martijn Kool. "Zero-dimensional Donaldson–Thomas invariants of Calabi–Yau 4-folds." Advances in Mathematics 338 (November 2018): 601–48. http://dx.doi.org/10.1016/j.aim.2018.09.011.

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45

Mozgovoy, Sergey, and Markus Reineke. "On the noncommutative Donaldson–Thomas invariants arising from brane tilings." Advances in Mathematics 223, no. 5 (2010): 1521–44. http://dx.doi.org/10.1016/j.aim.2009.10.001.

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46

Nagao, Kentaro. "Refined open noncommutative Donaldson–Thomas invariants for small crepant resolutions." Pacific Journal of Mathematics 254, no. 1 (2011): 173–209. http://dx.doi.org/10.2140/pjm.2011.254.173.

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47

Mozgovoy, Sergey. "On the motivic Donaldson–Thomas invariants of quivers with potentials." Mathematical Research Letters 20, no. 1 (2013): 107–18. http://dx.doi.org/10.4310/mrl.2013.v20.n1.a10.

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48

Chang, Huai Liang. "A vanishing result for Donaldson Thomas invariants of ℙ1 scroll". Acta Mathematica Sinica, English Series 30, № 12 (2014): 2079–84. http://dx.doi.org/10.1007/s10114-014-2730-6.

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49

Pasupuleti, Murali Krishna. "Unified Floer Theories for Quantum Topology of Four-Manifolds: Bridging Gauge Fields and Symplectic Cobordisms." International Journal of Academic and Industrial Research Innovations(IJAIRI) 05, no. 04 (2025): 357–66. https://doi.org/10.62311/nesx/rp3225.

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Abstract: Floer theories, originally formulated to study low-dimensional topology, have evolved to incorporate rich structures from gauge theory and symplectic geometry. Recent advances suggest the possibility of a unified framework connecting gauge-theoretic and symplectic invariants of four-manifolds. This paper critically interprets new results from topological gauge theories, symplectic Heegaard Floer foundations, and quantum cohomology, proposing a coherent structure to bridge gauge fields and symplectic cobordisms through unified Floer theories. Tables, conceptual diagrams, and comparati

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50

KIM, BUMSIG, and HWAYOUNG LEE. "WALL-CROSSINGS FOR TWISTED QUIVER BUNDLES." International Journal of Mathematics 24, no. 05 (2013): 1350038. http://dx.doi.org/10.1142/s0129167x13500389.

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Given a double quiver, we study homological algebra of twisted quiver sheaves with the moment map relation using the short exact sequence of Crawley-Boevey, Holland, Gothen, and King. Then in a certain one-parameter space of the stability conditions, we obtain a wall-crossing formula for the generalized Donaldson–Thomas invariants of the abelian category of framed twisted quiver sheaves on a smooth projective curve. To do so, we closely follow the approach of Chuang, Diaconescu and Pan in the ADHM quiver case, which makes use of the theory of Joyce and Song. The invariants virtually count fram

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