Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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LOCI OF RATIONAL CURVES OF SMALL DEGREE ON THE MODULI SPACE OF VECTOR BUNDLES

  • Received : 2009.08.05
  • Published : 2011.03.31
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Abstract

For a smooth algebraic curve C of genus g $\geq$ 4, let $SU_C$(r, d) be the moduli space of semistable bundles of rank r $\geq$ 2 over C with fixed determinant of degree d. When (r,d) = 1, it is known that $SU_C$(r, d) is a smooth Fano variety of Picard number 1, whose rational curves passing through a general point have degree $\geq$ r with respect to the ampl generator of Pic($SU_C$(r, d)). In this paper, we study the locus swept out by the rational curves on $SU_C$(r, d) of degree < r. As a by-product, we present another proof of Torelli theorem on $SU_C$(r, d).

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References

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Cited by

  1. SMALL RATIONAL CURVES ON THE MODULI SPACE OF STABLE BUNDLES vol.23, pp.08, 2012, https://doi.org/10.1142/S0129167X12500851