The Determinant Line Bundle over Moduli Spaces of Instantons on Abelian Surfaces
نویسنده
چکیده
We study the determinant line bundle over moduli space of stable bundles on abelian surfaces. We evaluate their analytic torsions. We extend Mukai's version of the Parseval Theorem to L 2 metrics on cohomology groups. We prove that the Mukai transform preserves the determinant line bundle as a hermitian line bundle. This is done by induction via the natural boundary of the moduli spaces.
منابع مشابه
A Fourier-Mukai approach to spectral data for instantons
We study U(r) instantons on elliptic surfaces with a section and show that they are in one-one correspondence with spectral data consisting of a curve in the dual elliptic surface and a line bundle on that curve. We use relative Fourier-Mukai transforms to analyse their properties and, in the case of the K3 and abelian surface, we show that the moduli space of instantons has a natural Lagrangia...
متن کاملInstanton Moduli as a Novel Map from Tori to K3-surfaces
A map is constructed from the moduli of hyper-KK ahler tori to hyper-KK ahler K3 surfaces which does not coincide with the Kummer map. The map takes a torus to the moduli space of SO(3) connections on a bundle with nontrivial rst Stiefel-Whitney class and rst Pontrjagin class equal to-4. This map is shown to intersect the Kummer moduli and also certain subvarieties of singular K3 surfaces. Our ...
متن کاملModuli Spaces of Stable Sheaves on Abelian Surfaces
Let X be a smooth projective surface defined over C and H an ample line bundle on X . If KX is trivial, that is, X is an abelian or a K3 surface, Mukai [Mu4] introduced a quite useful notion now called Mukai lattice (H(X,Z), 〈 , 〉), where H(X,Z) = ⊕iH(X,Z) and 〈x, y〉 = − ∫ X(x y) (see Defn. 1.1). 〈 , 〉 is an even unimodular bilinear form. For a coherent sheaf E on X , we can attach an element o...
متن کامل$PI$-extending modules via nontrivial complex bundles and Abelian endomorphism rings
A module is said to be $PI$-extending provided that every projection invariant submodule is essential in a direct summand of the module. In this paper, we focus on direct summands and indecomposable decompositions of $PI$-extending modules. To this end, we provide several counter examples including the tangent bundles of complex spheres of dimensions bigger than or equal to 5 and certain hyper ...
متن کامل0 A functional - analytic theory of vertex ( operator ) algebras , II
For a finitely-generated vertex operator algebra V of central charge c ∈ C, a locally convex topological completion HV is constructed. We construct on HV a structure of an algebra over the operad of the c 2 -th power Det c/2 of the determinant line bundle Det over the moduli space of genus-zero Riemann surfaces with ordered analytically parametrized boundary components. In particular, HV is a m...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1994