Excess dimension for secant loci in symmetric products of curves

• Autores: Marian Aprodu, Edoardo Sernesi
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 68, Fasc. 1, 2017, págs. 1-7
• Idioma: inglés
• DOI: 10.1007/s13348-016-0166-2
• Texto completo no disponible (Saber más ...)
• Resumen

  • We extend a result of W. Fulton, J. Harris and R. Lazarsfeld [6] to secant loci in symmetric products of curves. We compare three secant loci and prove that the dimensions of bigger loci can not be excessively larger than the dimension of smaller loci.

• Referencias bibliográficas
  • Aprodu, M., Nagel, J.: Koszul cohomology and algebraic geometry. University Lecture Series, vol. 52. American Mathematical Society, Providence...
  • Aprodu, M., Sernesi, E.: Secant spaces and syzygies of special line bundles on curves. Alg. Number Theory 9(3), 585–600 (2015)
  • Arbarello, E., Cornalba, M., Griffiths, P., Harris, J.: Geometry of algebraic curves, vol. I. Springer, New York (1984)
  • Coppens, M., Martens, G.: Secant spaces and Clifford’s theorem. Compos. Math. 78(2), 193–212 (1991)
  • Farkas, G., Kemeny, M.: The generic Green-Lazarsfeld secant conjecture. Invent. Math. 203(1), 265–301 (2016)
  • Fulton, W., Harris, J., Lazarsfeld, R.: Excess linear series on an algebraic curve. Proc. Am. Math. Soc. 92(3), 320–322 (1984)
  • Fulton, W., Lazarsfeld, R.: On the connectedness of degeneracy loci and special divisors. Acta Math. 146(1), 271–283 (1981)
  • Harris, J.: Algebraic geometry. A first course. Springer, New York (1992)
  • Kemeny, M.: The extremal secant conjecture for curve of arbitrary gonality. preprint arXiv:1512.00212 (2015)
  • Kempf, G.: Images of homogeneous vector bundles and varieties of complexes. Bull. Am. Math. Soc. 81(5), 900–901 (1975)