Hilbert functions of Koszul maps turn empirical chamber-wise polynomial formulae for line bundle cohomology on CICY threefolds into explicit analytic or finite-box certified statements.
Machine Learning Line Bundle Cohomologies of Hypersurfaces in Toric Varieties
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abstract
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.
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2026 1verdicts
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Hilbert Functions and Line Bundle Cohomology on CICY Threefolds
Hilbert functions of Koszul maps turn empirical chamber-wise polynomial formulae for line bundle cohomology on CICY threefolds into explicit analytic or finite-box certified statements.