대한수학회지 (Journal of the Korean Mathematical Society)

  • 제42권6호
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  • Pages.1279-1285
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  • 2005
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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BRILL-NOETHER DIVISORS ON THE MODULI SPACE OF CURVES AND APPLICATIONS

  • 발행 : 2005.11.01
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초록

Here we generalize previous work by Eisenbud-Harris and Farkas in order to prove that certain Brill-Noether divisors on the moduli space of curves have distinct supports. From this fact we deduce non-trivial regularity results for a higher co dimensional Brill-Noether locus and for the general $\frac{g+1}{2}$-gonal curve of odd genusg.

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참고문헌

  1. E. Arbarello, M. Cornalba, P. A. Griffiths, and J. Harris, Geometry of algebraic curves. Vol. I, Grundlehren Math. Wiss. 267 (1985)
  2. M.-C. Chang and Z. Ran, The Kodaira dimension of the moduli space of curves of genus 15, J. Differential Geom. 24 (1986), no. 2, 205-220 https://doi.org/10.4310/jdg/1214440435
  3. M. Cornalba and J. Harris, Divisor classes associated to families of stable varieties, with applications to the moduli space of curves, Ann. Sci. Ecole Norm. Sup. (4) 21 (1988), no. 3, 455-475 https://doi.org/10.24033/asens.1564
  4. M. Cornalba and J. Harris, Linear series on a general k-gonal curve, Abh. Math. Sem. Univ. Hamburg 69 (1999), 347-371 https://doi.org/10.1007/BF02940885
  5. M. Cornalba and J. Harris, Linear series on 4-gonal curves, Math. Nachr. 213 (2000), 35-55 https://doi.org/10.1002/(SICI)1522-2616(200005)213:1<35::AID-MANA35>3.0.CO;2-Z
  6. D. Edidin, Brill-Noether theory in codimension-two, J. Algebraic Geom. 2 (1993), no. 1, 25-67
  7. D. Eisenbud and J. Harris, Limit linear series: basic theory, Invent. Math. 85 (1986), no. 2, 337-371 https://doi.org/10.1007/BF01389094
  8. D. Eisenbud and J. Harris, Existence, decomposition, and limits of certain Weierstrass points, Invent. Math. 87 (1987), no. 3, 495-515 https://doi.org/10.1007/BF01389240
  9. D. Eisenbud and J. Harris, The Kodaira dimension of the moduli space of curves of genus ¸ 23, Invent. Math. 90 (1987), no. 2, 359-387 https://doi.org/10.1007/BF01388710
  10. D. Eisenbud and J. Harris, Irreducibility of some families of linear series with Brill-Noether number-1, Ann. Sci. Ecole Norm. Sup. (4) 22 (1989), no. 1, 33-53 https://doi.org/10.24033/asens.1574
  11. G. Farkas, The geometry of the moduli space of curves of genus 23, Math. Ann. 318 (2000), no. 1, 43-65 https://doi.org/10.1007/s002080000108
  12. J. Harris and D. Mumford, On the Kodaira dimension of the moduli space of curves, Invent. Math. 67 (1982), no. 1, 23-88 https://doi.org/10.1007/BF01393371
  13. F. Steffen, A generalized principal ideal theorem with an application to Brill-Noether theory, Invent. Math. 132 (1998), no. 1, 73-89 https://doi.org/10.1007/s002220050218

피인용 문헌

  1. Remarks on Brill–Noether divisors and Hilbert schemes vol.216, pp.2, 2012, https://doi.org/10.1016/j.jpaa.2011.06.019