For one-parameter degenerations of compact Kähler manifolds, we determine the asymptotic behavior of the first Chern form of the direct image of a Nakano semi-positive vector bundle twisted by the relative canonical bundle, when the direct image is equipped with the L2-metric.
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9 results for “L2-metric”
In this paper we introduce a projection method for the space of probability distributions based on the differential geometric approach to statistics. This method is based on a direct L2 metric as opposed to the usual Hellinger distance and the related Fisher Information metric. We explain how this apparatus can be used…
Study on a metric on Hermitian metrics space, proving diffeomorphisms and completeness.
problem Metric on space of Hermitian metrics on complex vector bundles.
method Compute metric spray, geodesics, curvature, and use Nash-Moser theorem.
result Metric completion of Hermitian metrics space is L2 integrable singular Hermitian metrics.
We prove that the metric on the direct image of an adjoint positive line bundle by a locally trivial submersion between projective manifolds is Nakano positive, under the assumption that the typical fiber has zero first Betti number. As a consequence, we get that the symmetric powers of an ample vector bundle ten…
It can be difficult to tell whether a trained generative model has learned to generate novel examples or has simply memorized a specific set of outputs. In published work, it is common to attempt to address this visually, for example by displaying a generated example and its nearest neighbor(s) in the training set (in,…
Modern datasets and models are notoriously difficult to explore and analyze due to their inherent high dimensionality and massive numbers of samples. Existing visualization methods which employ dimensionality reduction to two or three dimensions are often inefficient and/or ineffective for these datasets. This paper in…
We examine some differential geometric approaches to finding approximate solutions to the continuous time nonlinear filtering problem. Our primary focus is a new projection method for the optimal filter infinite dimensional Stochastic Partial Differential Equation (SPDE), based on the direct L2 metric and on a family o…
The paper studies the geometry of -moduli spaces and their embeddings.
problem Understanding the geometry and curvatures of -moduli spaces.
method New immersion of -moduli space into a homogeneous space and derivation of a formula for the fourth derivative of the potential.
result New insights into the geometry and curvatures of -moduli spaces.
The Lucas critique has exposed the problem of the trade-off between changes in monetary policy and structural breaks in economic time series. The search for and characterisation of such breaks has been a major econometric task ever since. We have developed an integral technique similar to CUSUM using an empirical model…