Stability of the Parabolic Picard Sheaf
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910567245021184 |
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| author | Arusha, C. Biswas, Indranil |
| author_facet | Arusha, C. Biswas, Indranil |
| contents | Let $X$ be a smooth irreducible complex projective curve of genus $g\,\geq\, 2$, and let $D\,=\,x_1+\dots+x_r$ be a reduced effective divisor on $X$. Denote by $U_α(L)$ the moduli space of stable parabolic vector bundles on $X$ of rank $n$, determinant $L$ of degree $d$ with flag type $\{\{k^i_j\}_{j=1}^{m_i}\}_{i=1}^r$. Assume that the greatest common divisor of the collection of integers $\{\text{degree}(L),\, \{\{k^i_j\}_{j=1}^{m_i}\}_{i=1}^r\}$ is $1$; this condition ensures that there is a Poincaré parabolic vector bundle on $X\times U_α(L)$. The direct image, to $U_α(L)$, of the vector bundle underlying the Poincaré parabolic vector bundle is called the parabolic Picard sheaf. We prove that the parabolic Picard sheaf is stable. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_18389 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of the Parabolic Picard Sheaf Arusha, C. Biswas, Indranil Algebraic Geometry 14F06, 14H60 Let $X$ be a smooth irreducible complex projective curve of genus $g\,\geq\, 2$, and let $D\,=\,x_1+\dots+x_r$ be a reduced effective divisor on $X$. Denote by $U_α(L)$ the moduli space of stable parabolic vector bundles on $X$ of rank $n$, determinant $L$ of degree $d$ with flag type $\{\{k^i_j\}_{j=1}^{m_i}\}_{i=1}^r$. Assume that the greatest common divisor of the collection of integers $\{\text{degree}(L),\, \{\{k^i_j\}_{j=1}^{m_i}\}_{i=1}^r\}$ is $1$; this condition ensures that there is a Poincaré parabolic vector bundle on $X\times U_α(L)$. The direct image, to $U_α(L)$, of the vector bundle underlying the Poincaré parabolic vector bundle is called the parabolic Picard sheaf. We prove that the parabolic Picard sheaf is stable. |
| title | Stability of the Parabolic Picard Sheaf |
| topic | Algebraic Geometry 14F06, 14H60 |
| url | https://arxiv.org/abs/2405.18389 |