Abstract
The aim of this paper is twofold. We first strongly improve our previous main result Choi et al. (Proc Am Math Soc 146(8):3233–3248, 2018, Theorem 3.1), 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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Acknowledgements
The authors thank KIAS and Dipartimento di Matematica Universita’ di Roma “Tor Vergata” for the warm atmosphere and hospitality during the collaboration and the preparation of this article. The authors are indebted to the referee for the careful reading of the first version of the paper and for valuable comments and suggestions which have certainly improved the readability of the paper.
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The first author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2016R1D1A3B03933342) and by Italian PRIN \(2015EYPTSB-011\)-Geomety of Algebraic varieties (Node Tor Vergata). The third author was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology (NRF-2016R1D1A1B03930844) and by Italian PRIN \(2015EYPTSB-011\)-Geomety of Algebraic varieties (Node Tor Vergata).
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Choi, Y., Flamini, F. & Kim, S. Moduli spaces of bundles and Hilbert schemes of scrolls over \(\nu \)-gonal curves. Collect. Math. 70, 295–321 (2019). https://doi.org/10.1007/s13348-018-0231-0
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DOI: https://doi.org/10.1007/s13348-018-0231-0