Abstract
We prove the existence of the moduli spaceM(n,d) of semistable generalised parabolic bundles (GPBs) of rankn, degreed of certain general type on a smooth curve. We study interesting cases of the moduli spacesM(n, d) and find explicit geometric descriptions for them in low ranks and genera. We define tensor products, symmetric powers etc. and the determinant of a GPB. We also define fixed determinant subvarietiesM L(n, d),L being a GPB of rank 1. We apply these results to study of moduli spaces of torsionfree sheaves on a reduced irreducible curveY with nodes and ordinary cusps as singularities. We also study relations among these moduli spaces (rank 2) as polarization varies over [0, 1].
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References
Bass Hyman, On the ubiquity of Gorenstein rings.Math. Z. 82 (1963) 8–28
Bhosle Usha N, Parabolic vector bundles on curves,Ark. Mat. 27 (1989) 15–22
Bhosle Usha N, Parabolic sheaves on higher dimensional varieties,Math. Ann. 293 (1992) 177–192
Bhosle Usha N, Generalised parabolic bundles and applications to torsionfree sheaves on nodal curves.Ark. Mat. 30 (1992) 187–215
Bhosle Usha N, Representations of the fundamental group and vector bundles,Math. Ann. 302 (1995) 601–608
Bhosle Usha N, Moduli of vector bundles on curves with many components, TIFR Preprint (1993)
Bhosle Usha N, Vector bundles of rank 2 and degree zero on a nodal hyperelliptic curve, To appear in Proc. Barcelona Conference (1994)
D’Souza Cyril, Compactification of generalised Jacobian.Proc. Indian Acad. Sci. 88A (1979) 419–457
Gieseker D, On the moduli of vector bundles on algebraic surfaces,Ann. Math 106 (1977) 45–60
Milne J S,Etale cohomology (Princeton University Press) (1980)
Mehta V B and Ramadas T R, Frobenius splittings of the moduli varieties of vector bundles on ordinary curves, TIFR Preprint (1993)
Newstead P E, Introduction to moduli problems and orbit spaces (Tata Institute, Bombay. Springer-Verlag) (1978)
Newstead P E, Moduli of torsionfree sheaves of rank 2 on a nodal curve of genus 2 (Preprint)
Rego C J Compactification of the space of vector bundles on a singular curve.Comment. Math. Helv. 57 (1982) 226–236
Ramadas T R and Narasimhan M S, Factorisation of generalised theta functions.I. Inventiones Math. 114 (1993) 565–623
Ramanan S, Orthogonal and spin bundles over hyperelliptic curves.Proc. Indian Acad. Sci. (Math. Sei.) 90 (1981) 151–166
Seshadri C S, Fibres vectoriels sur les courbes algebriques.Asterisque 96 (1982)
Seshadri C S and Mehta V B, Moduli of vector bundles on curves with parabolic structures.Math. Ann. 248 (1980) 205–239
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Bhosle, U.N. Generalized parabolic bundles and applications— II. Proc. Indian Acad. Sci. (Math. Sci.) 106, 403–420 (1996). https://doi.org/10.1007/BF02837696
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DOI: https://doi.org/10.1007/BF02837696