Moduli spaces of bundles and Hilbert schemes of scrolls over $\nu$-gonal curves

Youngook Choi; Flaminio Flamini; Seonja Kim

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arXiv · 1802.03956

Moduli spaces of bundles and Hilbert schemes of scrolls over $\nu$-gonal curves

Youngook Choi·Flaminio Flamini·Seonja Kim

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Abstract

The aim of this paper is two--fold. We first strongly improve our previous main result Theorem 3.1 in Arxiv 1702.00918v3 12Feb2018 ("Brill-Noether loci of rank two vector bundles on a general $\nu$-gonal curve"), concerning classification of irreducible components of the Brill--Noether locus parametrizing rank 2 semistable vector bundles of suitable degrees $d$, with at least $d-2g+4$ independent global sections, on a general $\nu$--gonal curve $C$ of genus $g$. We then uses this classification to study several properties of the Hilbert scheme of suitable surface scrolls in projective space, which turn out to be special and stable.

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BibTeX RIS

Youngook Choi, Flaminio Flamini, Seonja Kim. 2018-02-12. Moduli spaces of bundles and Hilbert schemes of scrolls over $\nu$-gonal curves. https://arxiv.org/abs/1802.03956

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