On Hilbert scheme of complete intersection on the biprojective
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913931095703552 |
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| author | Fontes, Aislan Leal Paixão, Maxwell |
| author_facet | Fontes, Aislan Leal Paixão, Maxwell |
| contents | The goal of this paper is to construct the Hilbert scheme of complete intersections in the biprojective space $X=\mathbb{P}^m\times\mathbb{P}^n$ and for this, we define a partial order on the bidegrees of the bihomogeneous forms. As a consequence of this construction, we computer explicitly the Hilbert scheme for curves of genus 7 and 8 listed in \cite{MUK95} and \cite{MUKIDE03} that are complete intersections. Finally, we construct the coarse moduli space of complete intersections in $\mathbb{P}^1\times\mathbb{P}^1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12546 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Hilbert scheme of complete intersection on the biprojective Fontes, Aislan Leal Paixão, Maxwell Algebraic Geometry 14D22, 14H10, 14C05, 14D20 The goal of this paper is to construct the Hilbert scheme of complete intersections in the biprojective space $X=\mathbb{P}^m\times\mathbb{P}^n$ and for this, we define a partial order on the bidegrees of the bihomogeneous forms. As a consequence of this construction, we computer explicitly the Hilbert scheme for curves of genus 7 and 8 listed in \cite{MUK95} and \cite{MUKIDE03} that are complete intersections. Finally, we construct the coarse moduli space of complete intersections in $\mathbb{P}^1\times\mathbb{P}^1$. |
| title | On Hilbert scheme of complete intersection on the biprojective |
| topic | Algebraic Geometry 14D22, 14H10, 14C05, 14D20 |
| url | https://arxiv.org/abs/2411.12546 |