Hodge classes on the moduli space of W(E_6)-covers and the geometry of A_6
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| Soggetti: | |
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| _version_ | 1866910403809771520 |
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| author | Alexeev, Valery Donagi, Ron Farkas, Gavril Izadi, Elham Ortega, Angela |
| author_facet | Alexeev, Valery Donagi, Ron Farkas, Gavril Izadi, Elham Ortega, Angela |
| contents | In previous work we showed that the Hurwitz space of W(E_6)-covers of the projective line branched over 24 points dominates via the Prym-Tyurin map the moduli space A_6 of principally polarized abelian 6-folds. Here we determine the 25 Hodge classes on the Hurwitz space of W(E_6)-covers corresponding to the 25 irreducible representations of the Weyl group W(E_6). This result has direct implications to the intersection theory of the toroidal compactification A_6. In the final part of the paper, we present an alternative, elementary proof of our uniformization result on A_6 via Prym-Tyurin varieties of type W(E_6). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_09691 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Hodge classes on the moduli space of W(E_6)-covers and the geometry of A_6 Alexeev, Valery Donagi, Ron Farkas, Gavril Izadi, Elham Ortega, Angela Algebraic Geometry In previous work we showed that the Hurwitz space of W(E_6)-covers of the projective line branched over 24 points dominates via the Prym-Tyurin map the moduli space A_6 of principally polarized abelian 6-folds. Here we determine the 25 Hodge classes on the Hurwitz space of W(E_6)-covers corresponding to the 25 irreducible representations of the Weyl group W(E_6). This result has direct implications to the intersection theory of the toroidal compactification A_6. In the final part of the paper, we present an alternative, elementary proof of our uniformization result on A_6 via Prym-Tyurin varieties of type W(E_6). |
| title | Hodge classes on the moduli space of W(E_6)-covers and the geometry of A_6 |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2107.09691 |