Hyperdeterminants from the $E_8$ Discriminant
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2018
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914092427509760 |
|---|---|
| author | Holweck, Frédéric Oeding, Luke |
| author_facet | Holweck, Frédéric Oeding, Luke |
| contents | We find expressions of the polynomials defining the dual varieties of Grassmannians $Gr(3,9)$ and $Gr(4,8)$ both in terms of the fundamental invariants and in terms of a generic semi-simple element. We project the polynomial defining the dual of the adjoint orbit of $E_{8}$, and obtain the polynomials of interest as factors. To find an expression of the $Gr(4,8)$ discriminant in terms of fundamental invariants, which has $15,942$ terms, we perform interpolation with mod-$p$ reduction and rational reconstruction. From these expressions for the discriminants of $Gr(3,9)$ and $Gr(4,8)$ we also obtain expressions for well-known hyperdeterminants of formats $3\times 3\times 3$ and $2\times 2\times 2\times 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1810_05857 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Hyperdeterminants from the $E_8$ Discriminant Holweck, Frédéric Oeding, Luke Algebraic Geometry We find expressions of the polynomials defining the dual varieties of Grassmannians $Gr(3,9)$ and $Gr(4,8)$ both in terms of the fundamental invariants and in terms of a generic semi-simple element. We project the polynomial defining the dual of the adjoint orbit of $E_{8}$, and obtain the polynomials of interest as factors. To find an expression of the $Gr(4,8)$ discriminant in terms of fundamental invariants, which has $15,942$ terms, we perform interpolation with mod-$p$ reduction and rational reconstruction. From these expressions for the discriminants of $Gr(3,9)$ and $Gr(4,8)$ we also obtain expressions for well-known hyperdeterminants of formats $3\times 3\times 3$ and $2\times 2\times 2\times 2$. |
| title | Hyperdeterminants from the $E_8$ Discriminant |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/1810.05857 |