scholarly journals Admissible subcategories in derived categories of moduli of vector bundles on curves

2019 ◽  
Vol 351 ◽  
pp. 653-675
Author(s):  
Pieter Belmans ◽  
Swarnava Mukhopadhyay
Keyword(s):  
Vector Bundles ◽  
Derived Categories ◽  
Moduli Of Vector Bundles

On the Cohomology of Moduli of Vector Bundles and the Tamagawa Number of SLn

2006 ◽  
Vol 58 (5) ◽  
pp. 1000-1025 ◽  
Author(s):  
Ajneet Dhillon
Keyword(s):  
Vector Bundles ◽  
Hodge Structure ◽  
Betti Numbers ◽  
Mixed Hodge Structure ◽  
Projective Curve ◽  
Ground Field ◽  
Smooth Projective Curve ◽  
Poincaré Polynomial ◽  
Moduli Stack ◽  
Moduli Of Vector Bundles

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.

scholarly journals QUILLEN EQUIVALENT MODELS FOR THE DERIVED CATEGORY OF FLATS AND THE RESOLUTION PROPERTY

2020 ◽  
pp. 1-19
Author(s):  
SERGIO ESTRADA ◽  
ALEXANDER SLÁVIK
Keyword(s):  
Vector Bundles ◽  
Derived Categories ◽  
Derived Category ◽  
Projective Modules ◽  
Dimensional Vector ◽  
Infinite Dimensional ◽  
Equivalent Models ◽  
Flat Modules ◽  
Quillen Equivalent ◽  
Resolution Property

We investigate the assumptions under which a subclass of flat quasicoherent sheaves on a quasicompact and semiseparated scheme allows us to ‘mock’ the homotopy category of projective modules. Our methods are based on module-theoretic properties of the subclass of flat modules involved as well as their behaviour with respect to Zariski localizations. As a consequence we get that, for such schemes, the derived category of flat quasicoherent sheaves is equivalent to the derived category of very flat quasicoherent sheaves. If, in addition, the scheme satisfies the resolution property then both derived categories are equivalent to the derived category of infinite-dimensional vector bundles. The equivalences are inferred from a Quillen equivalence between the corresponding models.

scholarly journals Rationality of moduli of vector bundles on curves

1999 ◽  
Vol 10 (4) ◽  
pp. 519-535 ◽  
Author(s):  
Alastair King ◽  
Aidan Schofield
Keyword(s):  
Vector Bundles ◽  
Moduli Of Vector Bundles

scholarly journals EQUATIONS OF THE MODULI OF HIGGS PAIRS AND INFINITE GRASSMANNIAN

2009 ◽  
Vol 20 (08) ◽  
pp. 1029-1055 ◽  
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.

scholarly journals Window shifts, flop equivalences and Grassmannian twists

2014 ◽  
Vol 150 (6) ◽  
pp. 942-978 ◽  
Author(s):  
Will Donovan ◽  
Ed Segal
Keyword(s):  
Vector Bundles ◽  
Derived Categories ◽  
Geometric Construction ◽  
Algebraic Construction ◽  
New Class ◽  
Spherical Twists

AbstractWe introduce a new class of autoequivalences that act on the derived categories of certain vector bundles over Grassmannians. These autoequivalences arise from Grassmannian flops: they generalize Seidel–Thomas spherical twists, which can be seen as arising from standard flops. We first give a simple algebraic construction, which is well suited to explicit computations. We then give a geometric construction using spherical functors which we prove is equivalent.

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