Loci of rational curves of small degree on the moduli space of vector bundles
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For a smooth algebraic curve C of genus g≥4, let SU_C(r,d) be the moduli space of semistable bundles of rank r≥2 over C with fixed dterminant 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 ≥ r with respect to the ample 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).
Abstract
For a smooth algebraic curve C of genus g≥4, let SU_C(r,d) be the moduli space of semistable bundles of rank r≥2 over C with fixed dterminant 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 ≥ r with respect to the ample 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).
참고문헌 (9)
- J.-M. Drezet, "Groupe de Picard des varietes de modules de fibres semi-stables sur les courbes algebriques", Invent. Math, 97(1), pp.53~94 (1989)
- J.-M. Hwang, "Hecke curves on the moduli space of vector bundles over an algebraic curve", Proceedings of the Symposium Algebraic Geometry in East Asia, pp.155~164 (2001)
- J. Kollar, "Rational Curves on Algebraic Varieties" (1996), Springer-Verlag
- H. Lange, "Zur Klassifikation von Regelmannigfaltigkeiten", Math. Ann, 262(4), pp.447~459 (1983)
- N. Mok, "Remarks on lines and minimal rational curves", Sciences in China Series A: Mathematics, 52(6), pp.1~16 (2009)
- M. S. Narasimhan, "Geometry of Hecke cycles. I, C. P. Ramanujam|a tribute", Tata Inst. Fund. Res. Studies in Math, 8, pp.291~345 (1978), Springer
- S. Ramanan, "The moduli spaces of vector bundles over an algebraic curve", Math. Ann, 200, pp.69~84 (1973)
- B. Russo, "On a conjecture of Lange", J. Algebraic Geom, 8(3), pp.483~496 (1999)
- X. Sun, "Minimal rational curves on moduli spaces of stable bundles", Math. Ann, 331(4), pp.925~937 (2005)