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October 10, 2025Forum of Mathematics PiOpen Access

The KSBA moduli space of stable log Calabi–Yau surfaces

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Every irreducible component of the ksba moduli space admits a finite cover by a projective toric variety, showcasing significant geometric structure.
This finding verifies a conjecture posed by Hacking–Keel–Yu regarding the nature of stable log calabi–yau surfaces within moduli spaces.
The proof integrates various advanced mathematical frameworks, including log smooth deformation theory, to establish a deeper understanding.
It highlights connections to punctured log gromov–witten theory and mirror symmetry, indicating collaboration among different mathematical disciplines.

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Research verifies a conjecture about ksba moduli space of stable log calabi–yau surfaces, suggesting new connections with projective toric varieties.

Alexeev et al. (2025) studied this question.

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Research verifies a conjecture about ksba moduli space of stable log calabi–yau surfaces, suggesting new connections with projective toric varieties.