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An explicit formula of the normalized Mumford form

発表形態：: 原著論文
主要業績：: 主要業績
単著・共著：: 単著
発表年月：: 2021年01月

DOI：: 10.1007/s11005-020-01339-0
会議属性：: 指定なし
査読：: 有り
リンク情報：

日本語フィールド

著者：

市川　尚志読み: イチカワ　タカシ

題名：

An explicit formula of the normalized Mumford form

発表情報：

Letters in Mathematical Physics 巻: 111

キーワード：

Normalized Mumford form, Moduli space of algebraic curves, Ramanujan delta function, Polyakov string measure

概要：

抄録：

We give an explicit formula of the normalized Mumford form which expresses the second tautological line bundle by the Hodge line bundle defined on the moduli space of algebraic curves of any genus. This formula is represented as an infinite product which is a higher genus version of the Ramanujan delta function under the trivialization by normalized abelian differentials and Eichler integrals of their products. Furthermore, this formula gives a universal expression of the normalized Mumford form as a computable power series with integral coefficients by the moduli parameters of algebraic curves. Therefore, one can describe the behavior of this form and hence of the Polyakov string measure around the Deligne-Mumford boundary.

英語フィールド

Author：

Takashi Ichikawa

Title：

An explicit formula of the normalized Mumford form

Announcement information:

Letters in Mathematical Physics Vol: 111

Keyword：

Normalized Mumford form, Moduli space of algebraic curves, Ramanujan delta function, Polyakov string measure

An abstract：