Relevant bibliographies by topics / Donaldson-Thomas invariant

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  2. Dissertations / Theses
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Academic literature on the topic 'Donaldson-Thomas invariant'

Author: Grafiati
Published: 2 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Donaldson-Thomas invariant"

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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Donaldson-Thomas invariant"

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Morrison, Andrew James. "Computing motivic Donaldson-Thomas invariants." Thesis, University of British Columbia, 2012. http://hdl.handle.net/2429/41935.

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This thesis develops a method (dimensional reduction) to compute motivic Donaldson--Thomas invariants. The method is then employed to compute these invariants in several different cases. Given a moduli scheme with a symmetric obstruction theory a Donaldson--Thomas type invariant can be defined by integrating Behrend's function over the scheme. Motivic Donaldson--Thomas theory aims to provide a more refined invariant associated to each such moduli space - a virtual motive. From the modern point of view motivic Donaldson-Thomas invariants should be defined for a three dimensional Calabi--Yau c
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Chang, Hua Liang. "Donaldson Thomas invariants of P¹ scroll /." May be available electronically:, 2007. http://proquest.umi.com/login?COPT=REJTPTU1MTUmSU5UPTAmVkVSPTI=&clientId=12498.

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Wu, Baosen. "A degeneration formula of Donaldson-Thomas invariants /." May be available electronically:, 2007. http://proquest.umi.com/login?COPT=REJTPTU1MTUmSU5UPTAmVkVSPTI=&clientId=12498.

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Beentjes, Sjoerd Viktor. "Crepant resolution conjecture for Donaldson-Thomas invariants via wall-crossing." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/33275.

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Let Y be a smooth complex projective Calabi{Yau threefold. Donaldson-Thomas invariants [Tho00] are integer invariants that virtually enumerate curves on Y. They are organised in a generating series DT(Y) that is interesting from a variety of perspectives. For example, well-known series in mathematics and physics appear in explicit computations. Furthermore, closer to the topic of this thesis, the generating series of birational Calabi-Yau threefolds determine one another [Cal16a]. The crepant resolution conjecture for Donaldson-Thomas invariants [BCY12] conjectures another such comparison resu
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Bussi, Vittoria. "Derived symplectic structures in generalized Donaldson-Thomas theory and categorification." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:54896cc4-b3fa-4d93-9fa9-2a842ad5e4df.

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This thesis presents a series of results obtained in [13, 18, 19, 23{25, 87]. In [19], we prove a Darboux theorem for derived schemes with symplectic forms of degree k < 0, in the sense of [142]. We use this to show that the classical scheme X = t<sub>0</sub>(X) has the structure of an algebraic d-critical locus, in the sense of Joyce [87]. Then, if (X, s) is an oriented d-critical locus, we prove in [18] that there is a natural perverse sheaf P·<sub>X,s</sub> on X, and in [25], we construct a natural motive MF<sub>X,s</sub>, in a certain quotient ring M<sup>μ</sup><sub>X</sub> of the μ-equiva
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Calabrese, John. "In the hall of the flop king : two applications of perverse coherent sheaves to Donaldson-Thomas invariants." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:b96b2bdd-8c79-4910-8795-f147bc8b2d16.

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This thesis contains two main results. The first is a comparison formula for the Donaldson-Thomas invariants of two (complex, smooth and projective) Calabi-Yau threefolds related by a flop; the second is a proof of the projective case of the Crepant Resolution Conjecture for Donaldson-Thomas invariants, as stated by Bryan, Cadman and Young. Both results rely on Bridgeland’s category of perverse coherent sheaves, which is the heart of a t-structure in the derived category of the given Calabi-Yau variety. The first formula is a consequence of various identities in an appropriate motivic Hall alg
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Beckwith, Olivia D. "On Toric Symmetry of P1 x P2." Scholarship @ Claremont, 2013. http://scholarship.claremont.edu/hmc_theses/46.

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Toric varieties are a class of geometric objects with a combinatorial structure encoded in polytopes. P1 x P2 is a well known variety and its polytope is the triangular prism. Studying the symmetries of the triangular prism and its truncations can lead to symmetries of the variety. Many of these symmetries permute the elements of the cohomology ring nontrivially and induce nontrivial relations. We discuss some toric symmetries of P1 x P2, and describe the geometry of the polytope of the corresponding blowups, and analyze the induced action on the cohomology ring. We exhaustively compute the to
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Ranganathan, Dhruv. "Gromov-Witten Theory of Blowups of Toric Threefolds." Scholarship @ Claremont, 2012. https://scholarship.claremont.edu/hmc_theses/31.

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We use toric symmetry and blowups to study relationships in the Gromov-Witten theories of $\mathbb{P}^3$ and $\mathbb{P}^1\!\times\!\mathbb{P}^1\!\times\!\mathbb{P}^1$. These two spaces are birationally equivalent via the common blowup space, the permutohedral variety. We prove an equivalence of certain invariants on blowups at only points of $\mathbb{P}^3$ and $\mathbb{P}^1\!\times\!\mathbb{P}^1\!\times\!\mathbb{P}^1$ by showing that these invariants descend from the blowup. Further, the permutohedral variety has nontrivial automorphisms of its cohomology coming from toric symmetry. These sym
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"Donaldson-Thomas theory for Calabi-Yau four-folds." 2013. http://library.cuhk.edu.hk/record=b5549280.

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令X 為個帶有凱勒形式(Kähler form ω) 以及全純四形式( holomorphic four- form Ω )的四維緊致卡拉比丘空間(Calabi-Yau manifolds) 。在一些假設條件下，通過研究Donaldson- Thomas方程所決定的模空間，我們定義了四維Donaldson-Thomas不變量。我們也對四維局部卡拉比丘空間(local Calabi-Yau four-folds) 定義了四維Donaldson-Thomas 不變量，並且將之聯繫到三維Fano空間的Donaldson- Thomas 不變量。在一些情況下，我們還研究了DT/GW不變量對應。最后，我們在模空間光滑時計算了一些四維Donaldson- Thomas不變量。<br>Let X be a complex four-dimensional compact Calabi-Yau manifold equipped with a Kahler form ω and a holomorphic four-form Ω. Under certain assumptions, we de ne Donaldson-Thomas type deformation invariants by studying the moduli space of the solutions of Donal
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Books on the topic "Donaldson-Thomas invariant"

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1977-, Song Yinan, ed. A theory of generalized Donaldson-Thomas invariants. American Mathematical Society, 2011.

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(Dietmar), Salamon D., ed. J-holomorphic curves and symplectic topology. 2nd ed. American Mathematical Society, 2012.

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3

Toda, Yukinobu. Recent Progress on the Donaldson-Thomas Theory: Wall-Crossing and Refined Invariants. Springer Singapore Pte. Limited, 2022.

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Hilbert Schemes of Points and Infinite Dimensional Lie Algebras. American Mathematical Society, 2018.

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String-Math 2015. American Mathematical Society, 2017.

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Surveys on Recent Developments in Algebraic Geometry. American Mathematical Society, 2017.

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Book chapters on the topic "Donaldson-Thomas invariant"

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Toda, Yukinobu. "Generalized Donaldson–Thomas Invariants." In SpringerBriefs in Mathematical Physics. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-7838-7_2.

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Toda, Yukinobu. "Cohomological Donaldson-Thomas Invariants." In SpringerBriefs in Mathematical Physics. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-7838-7_6.

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Zhu, Yuecheng. "Donaldson–Thomas Invariants and Wall-Crossing Formulas." In Calabi-Yau Varieties: Arithmetic, Geometry and Physics. Springer New York, 2015. http://dx.doi.org/10.1007/978-1-4939-2830-9_10.

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Toda, Yukinobu. "Wall-Crossing Formulas of Donaldson–Thomas Invariants." In SpringerBriefs in Mathematical Physics. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-7838-7_5.

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Toda, Yukinobu. "Donaldson–Thomas Invariants for Bridgeland Semistable Objects." In SpringerBriefs in Mathematical Physics. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-7838-7_4.

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van Garrel, Michel. "Introduction to Donaldson–Thomas and Stable Pair Invariants." In Calabi-Yau Varieties: Arithmetic, Geometry and Physics. Springer New York, 2015. http://dx.doi.org/10.1007/978-1-4939-2830-9_9.

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Toda, Yukinobu. "Donaldson–Thomas Invariants for Quivers with Super-Potentials." In SpringerBriefs in Mathematical Physics. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-7838-7_3.

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Toda, Yukinobu. "Donaldson–Thomas Invariants on Calabi–Yau 3-Folds." In SpringerBriefs in Mathematical Physics. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-7838-7_1.

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Kontsevich, Maxim, and Yan Soibelman. "Wall-Crossing Structures in Donaldson–Thomas Invariants, Integrable Systems and Mirror Symmetry." In Lecture Notes of the Unione Matematica Italiana. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06514-4_6.

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Ren, Jie, and Yan Soibelman. "Cohomological Hall Algebras, Semicanonical Bases and Donaldson–Thomas Invariants for 2-dimensional Calabi–Yau Categories (with an Appendix by Ben Davison)." In Algebra, Geometry, and Physics in the 21st Century. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-59939-7_7.

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