Skip to main content Accessibility help
×
Home

(t, ℓ)-STABILITY AND COHERENT SYSTEMS

  • L. BRAMBILA-PAZ (a1) and O. MATA-GUTIÉRREZ (a2)

Abstract

Let X be a non-singular irreducible complex projective curve of genus g ≥ 2. The concept of stability of coherent systems over X depends on a positive real parameter α, given then a (finite) family of moduli spaces of coherent systems. We use (t, ℓ)-stability to prove the existence of coherent systems over X that are α-stable for all allowed α > 0.

Copyright

References

Hide All
1.Arbarello, E., Cornalba, M. and Griffiths, P.A., Geometry of algebraic curves, Vol. I, Grundlehren der Mathematischen Wissenschaften, vol. 268 (1985), (Springer, Heidelberg, 1985).
2.Ballico, E., Coherent systems with many sections on projective curves. (English summary) Internat. J. Math. 17(3) (2006), 263267.
3.Bhosle, U. N., Brambila-Paz, L. Newstead, P. E., On coherent systems of type (n, d, n+1) on Petri curves, Manuscripta Math. 126 (2008), 409441.
4.Bhosle, U. N., Brambila-Paz, L. Newstead, P. E., On linear systems and a conjecture of D. C. Butler, Internat. J. Math. 26 (2015), 1550007, 18 p. doi:10.1142/S0129167X1550007X.
5.Bradlow, S. O. García-Prada, An application of coherent systems to a Brill–Noether problem, J Reine Angew. Math. 551 (2002), 123143.
6.Bradlow, S., García-Prada, O., Mercat, V., Muñoz, V. Newstead, P. E., On the geometry of moduli spaces of coherent systems on algebraic curves, Internat. J. Math. 18 (2007), 411453.
7.Bradlow, S., García-Prada, O., Muñoz, V. Newstead, P. E., Coherent systems and Brill–Noether Theory, Internat. J. Math. 14 (2003), 683733.
8.Brambila-Paz, L., Non-emptiness of moduli spaces of coherent systems, Internat. J. Math. 18(7) (2008), 777799.
9.Brambila-Paz, L., Grzegorczyk, I. and Newstead, P. E., Geography of Brill–Noether loci for small slopes, J. Alg. Geo. 6 (1997), 645669.
10.Brambila-Paz, L. and Lange, H., A stratification of the moduli space of vector bundles on curves, J. Reine Angew. Math 494 (1988), 173187.
11.Brambila-Paz, L., Mata-Gutiérrez, O., Ortega, A. and Newstead, P. E., On generated coherent systems and a conjecture of D. C. Butler, Internat. J. Math. 30(5) (2019). doi:10.1142/S0129167X19500241.
12.Brambila-Paz, L., Mercat, V., Newstead, P. E. and Ongay, F., Nonemptiness of Brill–Noether loci, Internat. J. Math. 11 (2000), 737760.
13.Butler, D. C., Birational maps of moduli of Brill–Noether pairs, preprint, arXiv:alg-geom/9705009.
14.Grothendieck, A. and Dieudonné, J., Éléments de géométrie algébrique, III, Pub. Math. IHES 17 France (1963).
15.Grzegorczyk, I. and Teixidor i Bigas, M., Brill–Noether Theory for stable bundles, in Moduli spaces and vector bundles. London Mathematical Society Note Series, vol. 359 (2009), 2950.
16.King, A. and Newstead, P. E., Moduli of Brill–Noether pairs on algebraic curves, Internat. J. Math. 6 (1995), 733748.
17.Lange, H. and Narasihman, M. S., Maximal subbundles of rank two vector bundles on curves, Math. Ann. 266 (1983), 5572.
18.Lange, H. and Newstead, P. E., Clifford’s theorem for coherent systems, Archiv der Mathematik 90(3) (2008), 209216.
19.Mata-Gutiérrez, O. and Neumann, F., Geometry of moduli stacks of (k, ℓ)-stable vector bundles over an algebraic curve, J. Geo. Phys. 111 (2017), 5470. doi:10.1016/j.geomphys.2016.10.003.
20.Narasimhan, M. S. and Ramanan, S., Deformation of the moduli space of vector bundles over an algebraic curve, Ann. of Math. 101(3) (1975), 391417.
21.Narasimhan, M. S. and Ramanan, S., Geometry of Hecke cycles - I, in C. P. Ramanujam - a tribute , Tata Institute of Fundamental Research Studies in Mathematics, vol. 8 (Springer-Verlag, Berlin-New York, 1978), pp. 291345.
22.Newstead, P. E., Existence of a-stable coherent systems on algebraic curves, Clay Math. Proc. 14 (2011), 121139.
23.Nitsure, N., Construction of Hilbert and Quot schemes, in Fundamental algebraic geometry – Grothendieck’s FGA explained (Fantachi, B. et al., Editor), Mathematical Surveys and Monographs, vol. 123, Part 2 (American Mathematical Society, France, 2005).
24.Raghavendra, N. and Vishwanath, P. A., Moduli of pairs and generalized theta divisors, Tohoku Math. J. 46 (1994), 321340.
25.Russo, B. and Teixidor i Bigas, M., On a conjecture of Lange, J. Alg. Geo. 8 (1999), 483496.
26.Teixidor i Bigas, M., Existence of coherent systems II, Int. J. Math. 19, 449 (2008), 12691283.
27.Teixidor i Bigas, M., Brill–Noether Theory for stable bundles, Duke Math. J. 62 (1991), 385400.

MSC classification

(t, ℓ)-STABILITY AND COHERENT SYSTEMS

  • L. BRAMBILA-PAZ (a1) and O. MATA-GUTIÉRREZ (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed