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Lazarsfeld–Mukai Bundles and Applications: II

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Bridging Algebra, Geometry, and Topology

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 96))

Abstract

This paper is a continuation of the work by Aprodu (Lazarsfeld-Mukai Bundles and Applications. Commutative Algebra, vol. 1–23. Springer, New York (2013)). We focus on non-K3 surfaces providing some improvements of known results.

Dedication to Alexandru Dimca and Ştefan Papadima

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References

  1. Aprodu, M.: On the vanishing of higher syzygies of curves. Math. Z. 241(1), 1–15 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Aprodu, M.: Remarks on syzygies of d-gonal curves. Math. Res. Lett. 12(2–3), 387–400 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  3. Aprodu, M.: Lazarsfeld-Mukai Bundles and Applications. Commutative Algebra, vol. 1–23. Springer, New York (2013)

    Google Scholar 

  4. Aprodu, M., Farkas, G.: Green’s conjecture for curves on arbitrary K3 surfaces. Compos. Math. 147(3), 839–851 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Arbarello, E., Cornalba, M.: Su una congetura di Petri. Comment. Math. Helv. 56(1), 1–38 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  6. Farkas, G., Ortega, A.: Higher rank Brill-Noether theory on sections of K3 surfaces. Int. J. Math. 23(7), 1250075, 18 pp (2012)

    Google Scholar 

  7. Green, M.: Koszul cohomology and the geometry of projective varietie. J. Differ. Geom. 19(1), 125–171 (1984)

    MATH  Google Scholar 

  8. Kim, H.: Moduli spaces of stable vector bundles on Enriques surfaces. Nagoya Math. J. 150, 85–94 (1998)

    MathSciNet  MATH  Google Scholar 

  9. Lazarsfeld, R.: Brill–Noether–Petri without degenerations. J. Differ. Geom. 23, 299–307 (1986)

    MathSciNet  MATH  Google Scholar 

  10. Lazarsfeld, R.: A sampling of vector bundle techniques in the study of linear series. Lectures on Riemann surfaces (Trieste, 1987), pp. 500–559. World Scientific, Teaneck (1989)

    Google Scholar 

  11. Lelli-Chiesa, M.: Green’s Conjecture for curves on rational surfaces with an anticanonical pencil. Math. Z. (2013). doi: 10.1007/s00209-013-1164-7

    Google Scholar 

  12. Mukai, S.: Biregular classification of Fano 3-folds and Fano manifolds of coindex 3. Proc. Natl. Acad. Sci. USA 86, 3000–3002 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  13. Pareschi, G.: A proof of Lazarsfeld’s theorem on curves on K3 surfaces. J. Algebraic Geom. 4(1), 195–200 (1995)

    MathSciNet  MATH  Google Scholar 

  14. Rasmussen, N.H., Zhou, S.: Pencils of small degree on curves on unnodal Enriques surfaces. arXiv:1307.5526

    Google Scholar 

  15. Voisin, C.: Green’s generic syzygy conjecture for curves of even genus lying on a K3 surface. J. Eur. Math. Soc. (JEMS) 4(4), 363–404 (2002)

    Google Scholar 

  16. Voisin, C.: Green’s canonical syzygy conjecture for generic curves of odd genus. Compos. Math. 141(5), 1163–1190 (2005)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work was partly supported by a Humboldt Fellowship and by the CNCS/UEFISCDI grant PN-II-ID-PCE-2011-3-0288 contract no. 132/05.10.2011. I would like to thank Humboldt Universität for hospitality and to G. Farkas for useful discussions on the topic.

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Authors and Affiliations

  1. “Simion Stoilow” Institute of Mathematics of the Romanian Academy, 1-764, RO-014700, Bucharest, Romania

    Marian Aprodu

Authors
  1. Marian Aprodu
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Correspondence to Marian Aprodu .

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Editors and Affiliations

  1. Faculty of Mathematics and Informatics, Ovidius University, Constanta, Constanta, Romania

    Denis Ibadula

  2. Department of Mathematics, University of Leuven, Leuven (Heverlee), Belgium

    Willem Veys

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Aprodu, M. (2014). Lazarsfeld–Mukai Bundles and Applications: II. In: Ibadula, D., Veys, W. (eds) Bridging Algebra, Geometry, and Topology. Springer Proceedings in Mathematics & Statistics, vol 96. Springer, Cham. https://doi.org/10.1007/978-3-319-09186-0_2

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