scholarly journals Infinite dimensional families of Calabi–Yau threefolds and moduli of vector bundles

2021 ◽  
Vol 225 (4) ◽  
pp. 106554
Author(s):  
Edoardo Ballico ◽  
Elizabeth Gasparim ◽  
Bruno Suzuki
Keyword(s):  
Vector Bundles ◽  
Infinite Dimensional ◽  
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

SUPER KRICHEVER FUNCTOR

1991 ◽  
Vol 02 (06) ◽  
pp. 741-760 ◽  
Author(s):  
MOTOHICO MULASE ◽  
JEFFREY M. RABIN
Keyword(s):  
Line Bundle ◽  
Vector Bundles ◽  
Vector Spaces ◽  
Contravariant Functor ◽  
Infinite Dimensional ◽  
Arbitrary Rank ◽  
Geometric Data

A supersymmetric generalization of the Krichever map is proposed. This map assigns injectively a point of an infinite dimensional super Grassmannian to a set of geometric data consisting of an arbitrary algebraic super manifold of dimension 1|1 defined over a field of any characteristic and a line bundle on it. The naturality of this map comes from the fact that it is obtained as the restriction of a contravariant functor to certain special objects. This functor gives an antiequivalence between the category of infinite dimensional super vector spaces satisfying the Fredholm condition together with their stabilizers, and the category of algebraic super curves and certain sheaves on them including all even vector bundles of arbitrary rank.

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