1,489 research outputs found
Harmonic Cheeger-Simons characters with applications
We initiate the study of harmonic Cheeger-Simons characters, with
applications to smooth versions of the Geometric Langlands program in the
abelian case.Comment: 13 pages, Latex2e, final version, Journal of Geometry and Physics (to
appear
Virtual refinements of the Vafa-Witten formula
We conjecture a formula for the generating function of virtual
-genera of moduli spaces of rank 2 sheaves on arbitrary surfaces with
holomorphic 2-form. Specializing the conjecture to minimal surfaces of general
type and to virtual Euler characteristics, we recover (part of) a formula of C.
Vafa and E. Witten.
These virtual -genera can be written in terms of descendent Donaldson
invariants. Using T. Mochizuki's formula, the latter can be expressed in terms
of Seiberg-Witten invariants and certain explicit integrals over Hilbert
schemes of points. These integrals are governed by seven universal functions,
which are determined by their values on and . Using localization we calculate these functions up to some
order, which allows us to check our conjecture in many cases.
In an appendix by H. Nakajima and the first named author, the virtual Euler
characteristic specialization of our conjecture is extended to include
-classes, thereby interpolating between Vafa-Witten's formula and Witten's
conjecture for Donaldson invariants.Comment: 44 pages. Published version. Appendix C by first named author and H.
Nakajim
Multivariable Hodge theoretical invariants of germs of plane curves
We describe methods for calculation of polytopes of quasiadjunction for plane
curve singularities which are invariants giving a Hodge theoretical refinement
of the zero sets of multivariable Alexander polynomials. In particular we
identify some hyperplanes on which all polynomials in multivariable Bernstein
ideal vanish
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