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math.AG2026
Motivic counting of curves on split quintic del Pezzo surfaces
Christian Bernert, Loïs Faisant, Jakob Glas
We prove the "all-the-heights'' version of the Batyrev--Manin--Peyre conjecture for split quintic del Pezzo surfaces, both for counting rational points over global function fields…
math.AG2024
Canonical singularities on moduli spaces of rational curves via the circle method
Jakob Glas
By developing a suitable version of the circle method, we show that the space of degree rational curves on a smooth hypersurface of degree has only canonical singularities…
math.AG2024
Terminal singularities of the moduli space of curves on low degree hypersurfaces and the circle method
Jakob Glas, Matthew Hase-Liu
We study the singularities of the moduli space of degree maps from smooth genus curves to an arbitrary smooth hypersurface of low degree. For large compared to , we…