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arXiv · 2209.07150

Degeneration of Hodge structures on I-surfaces

Stephen Coughlan·Marco Franciosi·Rita Pardini·Sönke Rollenske
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Abstract

Work of Green, Griffiths, Laza, and Robles suggests that the moduli space of (smoothable) stable surfaces should admit a natural stratification defined via Hodge theoretic data. In the case of stable surfaces with $K_X^2 = 1$ and $\chi(X) = 3$ we compute the Hodge type of all examples known to us and show that all predicted degenerations are geometrically realised.

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Stephen Coughlan, Marco Franciosi, Rita Pardini, Sönke Rollenske. 2022-09-15. Degeneration of Hodge structures on I-surfaces. https://arxiv.org/abs/2209.07150

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