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Seshadri constants on the self-product of an elliptic curve
The purpose of this paper is to study Seshadri constants on the self-product
of an elliptic curve . We provide explicit formulas for
computing the Seshadri constants of all ample line bundles on the surfaces
considered. As an application, we obtain a good picture of the behaviour of the
Seshadri function on the nef cone
Equivariance In Higher Geometry
We study (pre-)sheaves in bicategories on geometric categories: smooth
manifolds, manifolds with a Lie group action and Lie groupoids. We present
three main results: we describe equivariant descent, we generalize the plus
construction to our setting and show that the plus construction yields a
2-stackification for 2-prestacks. Finally we show that, for a 2-stack, the
pullback functor along a Morita-equivalence of Lie groupoids is an equivalence
of bicategories. Our results have direct applications to gerbes and 2-vector
bundles. For instance, they allow to construct equivariant gerbes from local
data and can be used to simplify the description of the local data. We
illustrate the usefulness of our results in a systematic discussion of
holonomies for unoriented surfaces.Comment: 42 pages, minor correction
Analysis of chromosomes in molecular tumor and radiation cytogenetics: Approaches, apllications, perspectives
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