Proceedings of the Japan Academy, Series A, Mathematical Sciences

Modular forms of weight $3m$ and elliptic modular surfaces

Shouhei Ma

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We prove that the graded ring of modular forms of weight divisible by 3 is naturally isomorphic to a certain log canonical ring of the associated elliptic modular surface. This extends the Shioda correspondence between weight 3 cusp forms and holomorphic 2-forms.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 95, Number 4 (2019), 31-36.

First available in Project Euclid: 1 April 2019

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Zentralblatt MATH identifier

Primary: 11F11: Holomorphic modular forms of integral weight
Secondary: 14J27: Elliptic surfaces 14J25: Special surfaces {For Hilbert modular surfaces, see 14G35}

Modular forms elliptic modular surfaces pluricanonical forms


Ma, Shouhei. Modular forms of weight $3m$ and elliptic modular surfaces. Proc. Japan Acad. Ser. A Math. Sci. 95 (2019), no. 4, 31--36. doi:10.3792/pjaa.95.31.

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