54 research outputs found
Bundles of generalized theta functions over abelian surfaces
We study the bundles of generalized theta functions constructed from moduli
spaces of sheaves over abelian surfaces. In degree 0, the splitting type of
these bundles is expressed in terms of indecomposable semihomogeneous factors.
Furthermore, Fourier-Mukai symmetries of the Verlinde bundles are found,
consistently with strange duality. Along the way, a transformation formula for
the theta bundles is derived, extending a theorem of Drezet-Narasimhan from
curves to abelian surfaces
On the intersection theory of the moduli space of rank two bundles
We give an algebro-geometric derivation of the known intersection theory on
the moduli space of stable rank 2 bundles of odd degree over a smooth curve of
genus g. We lift the computation from the moduli space to a Quot scheme, where
we obtain the intersections by equivariant localization with respect to a
natural torus action
Quot schemes of curves and surfaces: virtual classes, integrals, Euler characteristics
We compute tautological integrals over Quot schemes on curves and surfaces.
After obtaining several explicit formulas over Quot schemes of dimension 0
quotients on curves (and finding a new symmetry), we apply the results to
tautological integrals against the virtual fundamental classes of Quot schemes
of dimension 0 and 1 quotients on surfaces (using also universality, torus
localization, and cosection localization). The virtual Euler characteristics of
Quot schemes of surfaces, a new theory parallel to the Vafa-Witten Euler
characteristics of the moduli of bundles, is defined and studied. Complete
formulas for the virtual Euler characteristics are found in the case of
dimension 0 quotients on surfaces. Dimension 1 quotients are studied on K3
surfaces and surfaces of general type with connections to the Kawai-Yoshioka
formula and the Seiberg-Witten invariants respectively. The dimension 1 theory
is completely solved for minimal surfaces of general type admitting a
nonsingular canonical curve. Along the way, we find a new connection between
weighted tree counting and multivariate Fuss-Catalan numbers which is of
independent interest
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