4,818 research outputs found
-Riemann-Roch for singular complex curves
We present a comprehensive -theory for the -operator
on singular complex curves, including -versions of the Riemann-Roch
theorem and some applications.Comment: 19 page
Constraints on RG Flows from Holographic Entanglement Entropy
We examine the RG flow of a candidate c-function, extracted from the
holographic entanglement entropy of a strip-shaped region, for theories with
broken Lorentz invariance. We clarify the conditions on the geometry that lead
to a break-down of monotonic RG flows as is expected for generic
Lorentz-violating field theories. Nevertheless we identify a set of simple
criteria on the UV behavior of the geometry which guarantee a monotonic
c-function. Our analysis can thus be used as a guiding principle for the
construction of monotonic RG trajectories, and can also prove useful for
excluding possible IR behaviors of the theory.Comment: 5 pages, no figure
Modifications of torsion-free coherent analytic sheaves
We study the transformation of torsion-free coherent analytic sheaves under
proper modifications. More precisely, we study direct images of inverse image
sheaves, and torsion-free preimages of direct image sheaves. Under some
conditions, it is shown that torsion-free coherent sheaves can be realized as
the direct image of locally free sheaves under modifications. Thus, it is
possible to study coherent sheaves modulo torsion by reducing the problem to
study vector bundles on manifolds. We apply this to reduced ideal sheaves and
to the Grauert-Riemenschneider canonical sheaf of holomorphic n-forms.Comment: 28 pages; the article has been completely rewritten due to a wrong
statement in the first versio
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