scholarly journals Rationality of moduli of vector bundles on curves

1999 ◽  
Vol 10 (4) ◽  
pp. 519-535 ◽  
Author(s):  
Alastair King ◽  
Aidan Schofield
2006 ◽  
Vol 58 (5) ◽  
pp. 1000-1025 ◽  
Author(s):  
Ajneet Dhillon

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.


2009 ◽  
Vol 20 (08) ◽  
pp. 1029-1055 ◽  
Author(s):  
D. HERNÁNDEZ-SERRANO ◽  
J. M. MUÑOZ PORRAS ◽  
F. J. PLAZA MARTÍN

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.


2021 ◽  
pp. 2150041
Author(s):  
Suratno Basu ◽  
Sourav Das

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.


2016 ◽  
Vol 27 (07) ◽  
pp. 1650054 ◽  
Author(s):  
Daniel Greb ◽  
Julius Ross ◽  
Matei Toma

We survey recent progress in the study of moduli of vector bundles on higher-dimensional base manifolds. In particular, we discuss an algebro-geometric construction of an analogue for the Donaldson–Uhlenbeck compactification and explain how to use moduli spaces of quiver representations to show that Gieseker–Maruyama moduli spaces with respect to two different chosen polarizations are related via Thaddeus-flips through other “multi-Gieseker”-moduli spaces of sheaves. Moreover, as a new result, we show the existence of a natural morphism from a multi-Gieseker moduli space to the corresponding Donaldson–Uhlenbeck moduli space.


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