Geodesic
MOTIVIC DONALDSON–THOMAS THEORY AND THE ROLE OF ORIENTATION DATA
Glasgow mathematical journal, Tome 58 (2016) no. 1, pp. 229-262

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we introduce and motivate the concept of orientation data, as it appears in the framework for motivic Donaldson–Thomas theory built by Kontsevich and Soibelman. By concentrating on a single simple example we explain the role of orientation data in defining the integration map, a central component of the wall crossing formula. 
DAVISON, BEN. MOTIVIC DONALDSON–THOMAS THEORY AND THE ROLE OF ORIENTATION DATA. Glasgow mathematical journal, Tome 58 (2016) no. 1, pp. 229-262. doi: 10.1017/S0017089515000178
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[1] 1.Behrend, K., Donaldson-Thomas type invariants via microlocal geometry, Ann. Math. 170 (3) (2009), 1307–1338. Google Scholar | DOI

[2] 2.Behrend, K. and Fantechi, B., The intrinsic normal cone, Invent. Math. 128 (1) (1997), 45–88. Google Scholar | DOI

[3] 3.Behrend, K. and Fantechi, B., Symmetric obstruction theories and Hilbert schemes of points on threefolds, Algebra Number Theory 2 (3) (2008), 313–345. Google Scholar | DOI

[4] 4.Ben-Bassat, O., Brav, C., Bussi, V. and Joyce, D., A ‘Darboux Theorem’ for shifted symplectic structures on derived Artin stacks. Accepted for publication in Geometry and Topology, with applications, Available at: , 2013. Google Scholar | arXiv

[5] 5.Brav, C., Bussi, V., Dupont, D., Joyce, D. and Szendrői, B., Symmetries and stabilization for sheaves of vanishing cycles, Avaliable at: , 2012. Google Scholar | arXiv

[6] 6.Brav, C., Bussi, V. and Joyce, D., A ‘Darboux theorem’ for derived schemes with shifted symplectic structure, Available at: , 2013. Google Scholar | arXiv

[7] 7.Bussi, V., Joyce, D. and Meinhardt, S., On motivic vanishing cycles of critical loci, Available at: , 2013. Google Scholar | arXiv

[8] 8.Caldero, P. and Reineke, M., On the quiver grassmannian in the acyclic case, J. Pure and Appl. Algebr. 212 (11) (2008), 2369–2380. Google Scholar | DOI

[9] 9.Crawley-Boevey, W., Etingof, P. and Ginzburg, V., Noncommutative geometry and quiver algebras, Adv. Math. 209 (1) (2007), 274–336. Google Scholar | DOI

[10] 10.Davison, B., Invariance of orientation data for ind-constructible Calabi-Yau A categories under derived equivalence, Available at: . Google Scholar | arXiv

[11] 11.Denef, J. and Loeser, F., Motivic exponential integrals and a motivic Thom-Sebastiani theorem, Duke Math. J. 99 (2) (1999), 285–309. Google Scholar | DOI

[12] 12.Denef, J. and Loeser, F., Geometry on arc spaces of algebraic varieties, European Congress of Mathematics, (Barcelona, 2000), Progr. Math., vol. 201 (Birkhäuser, Basel, 2001), 327–348. Google Scholar

[13] 13.Efimov, A., Quantum cluster variables via vanishing cycles, Available at: . Google Scholar | arXiv

[14] 14.Ginzburg, V., Calabi-Yau algebras, Available at: , 2006. Google Scholar | arXiv

[15] 15.Huybrechts, D. and Lehn, M., The geometry of moduli spaces of sheaves, 2nd ed., Cambridge Mathematical Library (Cambridge University Press, Cambridge, 2010). Google Scholar | DOI

[16] 16.Joyce, D., Configurations in Abelian categories. I Basic properties and moduli stacks, Adv. Math. 203 (1) (2006), 194–255. Google Scholar | DOI

[17] 17.Joyce, D., Configurations in Abelian categories. II. Ringel-Hall algebras, Adv. Math. 210 (2) (2007), 635–706. Google Scholar | DOI

[18] 18.Joyce, D. and Song, Y., A theory of generalized Donaldson–Thomas invariants, Memories of the AMS (AMS, Providence, Rhode Island, 2012). Google Scholar | DOI

[19] 19.Kajiura, H., Noncommutative homotopy algebras associated with open strings, Rev. Math. Phys. 19 (1) (2007), 1–99. Google Scholar | DOI

[20] 20.Keller, B., Introduction to A-infinity algebras and modules, Homology Homotopy Appl. 3 (1) (2001), 1–35. Google Scholar | DOI

[21] 21.Kontsevich, M., Homological algebra of mirror symmetry, Proceedings of the International Congress of Mathematicians (Zurich) vol. 1 (Birkhäuser, 1995), 120–139. Google Scholar

[22] 22.Kontsevich, M. and Soibelman, Y., Notes on A -algebras, A -categories and non-commutative Geometry. I, Lecture Notes in Physics. 757 (2009), 1–67. Available at: http://arXiv.org:math/0606241, 2006. Google Scholar

[23] 23.Kontsevich, M. and Soibelman, Y., Stability structures, motivic Donaldson-Thomas invariants and cluster transformations, Available at: , 2008. Google Scholar | arXiv

[24] 24.Lefèvre-Hasegawa, K., Sur les A-catégories, PhD Thesis (Université Denis Diderot, 2003). Google Scholar

[25] 25.Looijenga, E., Motivic measures, Séminaire Bourbaki, Vol. 1999/2000, Astérisque no. 276, (2002), 267–297. Google Scholar

[26] 26.Lu, D., Palmieri, J., Wu, Q. and Zhang, J., Koszul equivalences in A-algebras, New York J. Math. 14 (2008), 325–378. Google Scholar

[27] 27.Parusiński, A. and Pragacz, P., Characteristic classes of hypersurfaces and characteristic cycles, J. Alg. Geom. 10 (1) (2001), 63–79. Google Scholar

[28] 28.Segal, E., The A deformation theory of a point and the derived categories of local Calabi-Yaus, J. Algebra 320 (8) (2008), 3232–3268. Google Scholar | DOI

[29] 29.Szendrői, B., Non-commutative Donaldson-Thomas theory and the conifold, Geom. Topol. 12 (2) (2008), 1171–1202. Google Scholar | DOI

[30] 30.Thomas, R., Gauge theory on Calabi-Yau manifolds, PhD Thesis (Oxford University, 1997). Google Scholar

[31] 31.Quy Thuong, L., Proofs of the integral identity conjecture over algebraically closed fields, Duke Math. J. 164 (1) (2015), 157–194. Available at: . Google Scholar | arXiv

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