Intrinsic Donaldson-Thomas theory. II. Stability measures and invariants
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| Format: | Preprint |
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2025
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| _version_ | 1866915176363589632 |
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| author | Bu, Chenjing Núñez, Andrés Ibáñez Kinjo, Tasuki |
| author_facet | Bu, Chenjing Núñez, Andrés Ibáñez Kinjo, Tasuki |
| contents | This is the second paper in a series on intrinsic Donaldson-Thomas theory, a framework for studying the enumerative geometry of general algebraic stacks.
In this paper, we present the construction of Donaldson-Thomas invariants for general $(-1)$-shifted symplectic derived Artin stacks, generalizing the constructions of Joyce-Song and Kontsevich-Soibelman for moduli stacks of objects in $3$-Calabi-Yau abelian categories. Our invariants are defined using rings of motives, and depend intrinsically on the stack, together with a set of combinatorial data similar to a stability condition, called a stability measure on the component lattice of the stack. For our invariants to be well-defined, we prove a generalization of Joyce's no-pole theorem to general stacks, using a simpler and more conceptual argument than the original proof in the abelian category case.
Further properties and applications of these invariants, such as wall-crossing formulae, will be discussed in a forthcoming paper. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_20515 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Intrinsic Donaldson-Thomas theory. II. Stability measures and invariants Bu, Chenjing Núñez, Andrés Ibáñez Kinjo, Tasuki Algebraic Geometry This is the second paper in a series on intrinsic Donaldson-Thomas theory, a framework for studying the enumerative geometry of general algebraic stacks. In this paper, we present the construction of Donaldson-Thomas invariants for general $(-1)$-shifted symplectic derived Artin stacks, generalizing the constructions of Joyce-Song and Kontsevich-Soibelman for moduli stacks of objects in $3$-Calabi-Yau abelian categories. Our invariants are defined using rings of motives, and depend intrinsically on the stack, together with a set of combinatorial data similar to a stability condition, called a stability measure on the component lattice of the stack. For our invariants to be well-defined, we prove a generalization of Joyce's no-pole theorem to general stacks, using a simpler and more conceptual argument than the original proof in the abelian category case. Further properties and applications of these invariants, such as wall-crossing formulae, will be discussed in a forthcoming paper. |
| title | Intrinsic Donaldson-Thomas theory. II. Stability measures and invariants |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2502.20515 |