Logarithmic Cobordism and Donaldson-Thomas Invariants
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918253597556736 |
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| author | Guzman, Jose |
| author_facet | Guzman, Jose |
| contents | We introduce a logarithmic cobordism $ω^{\text{Log}}$ ring of pairs $(X,D)$ of varieties equipped with a simple normal crossings divisor $D\subset X$, analogous to the algebraic cobordism ring $ω^{\text{LP}}$ of Levine-Pandharipande, and we provide an application to logarithmic DT invariants. We also prove prove that if we impose the relation $(X',D') = (X,D)$ for $(X',D')\rightarrow (X,D)$ a logarithmic modification, then the new "logarithmic+modification" cobordism ring $ω^{\text{Log+Mod}}$ collapses to the algebraic cobordism ring of Levine-Pandharipande: $ω^{\text{LP}}\cong ω^{\text{Log+Mod}}$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_15085 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Logarithmic Cobordism and Donaldson-Thomas Invariants Guzman, Jose Algebraic Geometry We introduce a logarithmic cobordism $ω^{\text{Log}}$ ring of pairs $(X,D)$ of varieties equipped with a simple normal crossings divisor $D\subset X$, analogous to the algebraic cobordism ring $ω^{\text{LP}}$ of Levine-Pandharipande, and we provide an application to logarithmic DT invariants. We also prove prove that if we impose the relation $(X',D') = (X,D)$ for $(X',D')\rightarrow (X,D)$ a logarithmic modification, then the new "logarithmic+modification" cobordism ring $ω^{\text{Log+Mod}}$ collapses to the algebraic cobordism ring of Levine-Pandharipande: $ω^{\text{LP}}\cong ω^{\text{Log+Mod}}$ |
| title | Logarithmic Cobordism and Donaldson-Thomas Invariants |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2510.15085 |