Motivic Donaldson–Thomas invariants of some quantized threefolds
This paper is motivated by the question of howmotivic Donaldson–Thomas invariants behave in families. We compute the invariants for some simple families of noncommutative Calabi–Yau threefolds, defined by quivers with homogeneous potentials. These families give deformation quantizations of affine th...
| Những tác giả chính: | , , , |
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| Định dạng: | Journal article |
| Được phát hành: |
European Mathematical Society
2017
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| _version_ | 1826305515514232832 |
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| author | Cazzaniga, A Morrison, A Pym, B Szendroi, B |
| author_facet | Cazzaniga, A Morrison, A Pym, B Szendroi, B |
| author_sort | Cazzaniga, A |
| collection | OXFORD |
| description | This paper is motivated by the question of howmotivic Donaldson–Thomas invariants behave in families. We compute the invariants for some simple families of noncommutative Calabi–Yau threefolds, defined by quivers with homogeneous potentials. These families give deformation quantizations of affine three-space, the resolved conifold, and the resolution of the transversal An-singularity. It turns out that their invariants are generically constant, but jump at special values of the deformation parameter, such as roots of unity. The corresponding generating series are written in closed form, as plethystic exponentials of simple rational functions. While our results are limited by the standard dimensional reduction techniques that we employ, they nevertheless allow us to conjecture formulae for more interesting cases, such as the elliptic Sklyanin algebras. |
| first_indexed | 2024-03-07T06:34:00Z |
| format | Journal article |
| id | oxford-uuid:f6fbcff0-47e4-4377-accd-c85a7a4ff67a |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:34:00Z |
| publishDate | 2017 |
| publisher | European Mathematical Society |
| record_format | dspace |
| spelling | oxford-uuid:f6fbcff0-47e4-4377-accd-c85a7a4ff67a2022-03-27T12:39:09ZMotivic Donaldson–Thomas invariants of some quantized threefoldsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f6fbcff0-47e4-4377-accd-c85a7a4ff67aSymplectic Elements at OxfordEuropean Mathematical Society2017Cazzaniga, AMorrison, APym, BSzendroi, BThis paper is motivated by the question of howmotivic Donaldson–Thomas invariants behave in families. We compute the invariants for some simple families of noncommutative Calabi–Yau threefolds, defined by quivers with homogeneous potentials. These families give deformation quantizations of affine three-space, the resolved conifold, and the resolution of the transversal An-singularity. It turns out that their invariants are generically constant, but jump at special values of the deformation parameter, such as roots of unity. The corresponding generating series are written in closed form, as plethystic exponentials of simple rational functions. While our results are limited by the standard dimensional reduction techniques that we employ, they nevertheless allow us to conjecture formulae for more interesting cases, such as the elliptic Sklyanin algebras. |
| spellingShingle | Cazzaniga, A Morrison, A Pym, B Szendroi, B Motivic Donaldson–Thomas invariants of some quantized threefolds |
| title | Motivic Donaldson–Thomas invariants of some quantized threefolds |
| title_full | Motivic Donaldson–Thomas invariants of some quantized threefolds |
| title_fullStr | Motivic Donaldson–Thomas invariants of some quantized threefolds |
| title_full_unstemmed | Motivic Donaldson–Thomas invariants of some quantized threefolds |
| title_short | Motivic Donaldson–Thomas invariants of some quantized threefolds |
| title_sort | motivic donaldson thomas invariants of some quantized threefolds |
| work_keys_str_mv | AT cazzanigaa motivicdonaldsonthomasinvariantsofsomequantizedthreefolds AT morrisona motivicdonaldsonthomasinvariantsofsomequantizedthreefolds AT pymb motivicdonaldsonthomasinvariantsofsomequantizedthreefolds AT szendroib motivicdonaldsonthomasinvariantsofsomequantizedthreefolds |