On moduli of vector bundles on rational surfaces

AbstractWe compute some Hodge and Betti numbers of the moduli space of stable rank r, degree d vector bundles on a smooth projective curve. We do not assume r and d are coprime. In the process we equip the cohomology of an arbitrary algebraic stack with a functorial mixed Hodge structure. This Hodge structure is computed in the case of the moduli stack of rank r, degree d vector bundles on a curve. Our methods also yield a formula for the Poincaré polynomial of the moduli stack that is valid over any ground field. In the last section we use the previous sections to give a proof that the Tamagawa number of SLn is one.

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Rationality of moduli of vector bundles on curves

Indagationes Mathematicae ◽

10.1016/s0019-3577(00)87905-7 ◽

1999 ◽

Vol 10 (4) ◽

pp. 519-535 ◽

Cited By ~ 23

Author(s):

Alastair King ◽

Aidan Schofield

Keyword(s):

Vector Bundles ◽

Moduli Of Vector Bundles

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Moduli of Vector Bundles with Odd c 1 on Surfaces with q = p g = 0

American Journal of Mathematics ◽

10.2307/2374705 ◽

1992 ◽

Vol 114 (2) ◽

pp. 297 ◽

Cited By ~ 4

Author(s):

Dieter Kotschick

Keyword(s):

Vector Bundles ◽

Moduli Of Vector Bundles

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On the new compactification of moduli of vector bundles on a surface. II

Sbornik Mathematics ◽

10.1070/sm2009v200n03abeh004002 ◽

2009 ◽

Vol 200 (3) ◽

pp. 405-427 ◽

Cited By ~ 8

Author(s):

Nadezhda V Timofeeva

Keyword(s):

Vector Bundles ◽

Moduli Of Vector Bundles

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EQUATIONS OF THE MODULI OF HIGGS PAIRS AND INFINITE GRASSMANNIAN

International Journal of Mathematics ◽

10.1142/s0129167x09005637 ◽

2009 ◽

Vol 20 (08) ◽

pp. 1029-1055 ◽

Cited By ~ 1

Author(s):

D. HERNÁNDEZ-SERRANO ◽

J. M. MUÑOZ PORRAS ◽

F. J. PLAZA MARTÍN

Keyword(s):

Fixed Point ◽

Moduli Space ◽

Vector Bundles ◽

Higgs Field ◽

Projective Curve ◽

Smooth Projective Curve ◽

Spectral Cover ◽

Relative Version ◽

Moduli Of Vector Bundles

In this paper the moduli space of Higgs pairs over a fixed smooth projective curve with extra formal data is defined and is endowed with a scheme structure. We introduce a relative version of the Krichever map using a fibration of Sato Grassmannians and show that this map is injective. This, together with the characterization of the points of the image of the Krichever map, allows us to prove that this moduli space is a closed subscheme of the product of the moduli of vector bundles (with formal extra data) and a formal anologue of the Hitchin base. This characterization also provides us with a method for explicitly computing KP-type equations that describe the moduli space of Higgs pairs. Finally, for the case where the spectral cover is totally ramified at a fixed point of the curve, these equations are given in terms of the characteristic coefficients of the Higgs field.

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A Torelli type theorem for nodal curves

International Journal of Mathematics ◽

10.1142/s0129167x21500415 ◽

2021 ◽

pp. 2150041

Author(s):

Suratno Basu ◽

Sourav Das

Keyword(s):

Moduli Space ◽

Vector Bundles ◽

Type Theorem ◽

Projective Curve ◽

Fixed Degree ◽

Smooth Projective Curve ◽

Nodal Curve ◽

Normal Crossing ◽

Moduli Of Vector Bundles ◽

Fixed Rank

The moduli space of Gieseker vector bundles is a compactification of moduli of vector bundles on a nodal curve. This moduli space has only normal-crossing singularities and it provides flat degeneration of the moduli of vector bundles over a smooth projective curve. We prove a Torelli type theorem for a nodal curve using the moduli space of stable Gieseker vector bundles of fixed rank (strictly greater than [Formula: see text]) and fixed degree such that rank and degree are co-prime.

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