Semi-homogeneous vector bundles on abelian varieties: moduli spaces and their tropicalization
A. Gross, I. Kaur, M. Ulirsch, A. Werner, Moduli 3 (2026).
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Journal Article
| Published
| English
Author
Gross, Andreas;
Kaur, Inder;
Ulirsch, MartinLibreCat;
Werner, Annette
Abstract
<jats:title>Abstract</jats:title>
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Let
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<jats:tex-math>$A$</jats:tex-math>
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</jats:inline-formula>
be an abelian variety with totally degenerate reduction over a non-Archimedean field. We describe the moduli space of semi-homogeneous vector bundles on
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<jats:tex-math>$A$</jats:tex-math>
</jats:alternatives>
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from the perspective of non-Archimedean uniformization and show that the essential skeleton may be identified with a tropical analogue of this moduli space. For
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<jats:alternatives>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S2949764726100228_inline3.png"/>
<jats:tex-math>$H=0$</jats:tex-math>
</jats:alternatives>
</jats:inline-formula>
our moduli space may be identified with the moduli space
<jats:inline-formula>
<jats:alternatives>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S2949764726100228_inline4.png"/>
<jats:tex-math>$M_{0,r}(A)$</jats:tex-math>
</jats:alternatives>
</jats:inline-formula>
of semi-stable vector bundles with vanishing Chern classes on
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<jats:alternatives>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S2949764726100228_inline5.png"/>
<jats:tex-math>$A$</jats:tex-math>
</jats:alternatives>
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. In this case we construct a surjective analytic morphism from the character variety of the analytic fundamental group of
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<jats:tex-math>$A$</jats:tex-math>
</jats:alternatives>
</jats:inline-formula>
onto
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<jats:alternatives>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S2949764726100228_inline7.png"/>
<jats:tex-math>$M_{0,r}(A)$</jats:tex-math>
</jats:alternatives>
</jats:inline-formula>
, which naturally tropicalizes. One may view this construction as a non-Archimedean uniformization of
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<jats:alternatives>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S2949764726100228_inline8.png"/>
<jats:tex-math>$M_{0,r}(A)$</jats:tex-math>
</jats:alternatives>
</jats:inline-formula>
.
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Publishing Year
Journal Title
Moduli
Volume
3
Article Number
e8
LibreCat-ID
Cite this
Gross A, Kaur I, Ulirsch M, Werner A. Semi-homogeneous vector bundles on abelian varieties: moduli spaces and their tropicalization. Moduli. 2026;3. doi:10.1017/S2949764726100228
Gross, A., Kaur, I., Ulirsch, M., & Werner, A. (2026). Semi-homogeneous vector bundles on abelian varieties: moduli spaces and their tropicalization. Moduli, 3, Article e8. https://doi.org/10.1017/S2949764726100228
@article{Gross_Kaur_Ulirsch_Werner_2026, title={Semi-homogeneous vector bundles on abelian varieties: moduli spaces and their tropicalization}, volume={3}, DOI={10.1017/S2949764726100228}, number={e8}, journal={Moduli}, publisher={Cambridge University Press (CUP)}, author={Gross, Andreas and Kaur, Inder and Ulirsch, Martin and Werner, Annette}, year={2026} }
Gross, Andreas, Inder Kaur, Martin Ulirsch, and Annette Werner. “Semi-Homogeneous Vector Bundles on Abelian Varieties: Moduli Spaces and Their Tropicalization.” Moduli 3 (2026). https://doi.org/10.1017/S2949764726100228.
A. Gross, I. Kaur, M. Ulirsch, and A. Werner, “Semi-homogeneous vector bundles on abelian varieties: moduli spaces and their tropicalization,” Moduli, vol. 3, Art. no. e8, 2026, doi: 10.1017/S2949764726100228.
Gross, Andreas, et al. “Semi-Homogeneous Vector Bundles on Abelian Varieties: Moduli Spaces and Their Tropicalization.” Moduli, vol. 3, e8, Cambridge University Press (CUP), 2026, doi:10.1017/S2949764726100228.
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