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arXiv · 2301.02550

Differential forms on universal K3 surfaces

Shouhei Ma
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Abstract

We give a vanishing and classification result for holomorphic differential forms on smooth projective models of the moduli spaces of pointed K3 surfaces. We prove that there is no nonzero holomorphic k-form for 0 19. In the remaining cases, we give an isomorphism between the space of holomorphic k-forms with that of vector-valued modular forms (9 18) for the modular group. These results are in fact proved in the generality of lattice-polarization.

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Shouhei Ma. 2023-01-06. Differential forms on universal K3 surfaces. https://doi.org/10.1017/s0305004124000100

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