Proceedings of the Japan Academy, Series A, Mathematical Sciences

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

Shouhei Ma

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 1 April 2019

Permanent link to this document
https://projecteuclid.org/euclid.pja/1554084020

Digital Object Identifier
doi:10.3792/pjaa.95.31

Mathematical Reviews number (MathSciNet)
MR3934983

Zentralblatt MATH identifier
07121251

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

Keywords
Modular forms elliptic modular surfaces pluricanonical forms

Citation

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. https://projecteuclid.org/euclid.pja/1554084020


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References

  • F. Diamond and J. Shurman, A first course in modular forms, Graduate Texts in Mathematics, 228, Springer-Verlag, New York, 2005.
  • S. Ishii, Introduction to singularities, Springer, Tokyo, 2014.
  • T. Shioda, On elliptic modular surfaces, J. Math. Soc. Japan 24 (1972), 20–59.