Characteristic Currents on Cohesive Modules
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908091830763520 |
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| author | Han, Zhaobo Tom |
| author_facet | Han, Zhaobo Tom |
| contents | Let $\mathcal{F}$ be a coherent sheaf on a complex variety $X$ that has a locally free resolution $E^{\bullet}$. In [19], the authors constructed a pseudomeromorphic current whose support is contained in $supp(E^{\bullet})$ that represents products of Chern classes of $\mathcal{F}.$ In this paper, we show that their construction works for general de-Rham characteristic classes and then generalize it to represent products (in de-Rham cohomology) of characteristic forms of cohesive modules defined by Block. Finally, we state a corollary to a transgression result in [16] that show that it is sufficient to only use the degree-$0$ and degree-$1$ parts of the superconnection to construct currents that represent characteristic forms of cohesive modules in the Bott-Chern cohomology. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_09439 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characteristic Currents on Cohesive Modules Han, Zhaobo Tom Algebraic Geometry Algebraic Topology Differential Geometry Let $\mathcal{F}$ be a coherent sheaf on a complex variety $X$ that has a locally free resolution $E^{\bullet}$. In [19], the authors constructed a pseudomeromorphic current whose support is contained in $supp(E^{\bullet})$ that represents products of Chern classes of $\mathcal{F}.$ In this paper, we show that their construction works for general de-Rham characteristic classes and then generalize it to represent products (in de-Rham cohomology) of characteristic forms of cohesive modules defined by Block. Finally, we state a corollary to a transgression result in [16] that show that it is sufficient to only use the degree-$0$ and degree-$1$ parts of the superconnection to construct currents that represent characteristic forms of cohesive modules in the Bott-Chern cohomology. |
| title | Characteristic Currents on Cohesive Modules |
| topic | Algebraic Geometry Algebraic Topology Differential Geometry |
| url | https://arxiv.org/abs/2404.09439 |