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Machine learning line bundle cohomologies of hypersurfaces in toric varieties. (English) Zbl 1406.14001
Summary: Different techniques from machine learning are applied to the problem of computing line bundle cohomologies of (hypersurfaces in) toric varieties. While a naive approach of training a neural network to reproduce the cohomologies fails in the general case, by inspecting the underlying functional form of the data we propose a second approach. The cohomologies depend in a piecewise polynomial way on the line bundle charges. We use unsupervised learning to separate the different polynomial phases. The result is an analytic formula for the cohomologies. This can be turned into an algorithm for computing analytic expressions for arbitrary (hypersurfaces in) toric varieties.

14-04 Software, source code, etc. for problems pertaining to algebraic geometry
14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
cohomCalg; GitHub
Full Text: DOI
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