Machine Learning and Algebraic Approaches towards Complete Matter Spectra in 4d F-theory

Understand

Motivated by engineering vector-like (Higgs) pairs in the spectrum of 4d F-theory compactifications, we combine machine learning and algebraic geometry techniques to analyze line bundle cohomologies on families of holomorphic curves.

• To quantify jumps of these cohomologies, we first generate 1.8 million pairs of line bundles and curves embedded in $dP_3$, for which we compute the cohomologies.
• A white-box machine learning approach trained on this data provides intuition for jumps due to curve splittings, which we use to construct additional vector-like Higgs-pairs in an F-Theory toy model.
• We also find that, in order to explain quantitatively the full dataset, further tools from algebraic geometry, in particular Brill--Noether theory, are required.