Hyperbolic 2-spheres with conical singularities, accessory parameters and Kähler metrics on M0,n

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Hyperbolic 2-spheres with conical singularities, accessory parameters and Kähler metrics on M0,n. / Takhtajan, Leon; Zograf, Peter.

In: Transactions of the American Mathematical Society, Vol. 355, No. 5, 01.05.2003, p. 1857-1867.

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Author

Takhtajan, Leon ; Zograf, Peter. / Hyperbolic 2-spheres with conical singularities, accessory parameters and Kähler metrics on M0,n. In: Transactions of the American Mathematical Society. 2003 ; Vol. 355, No. 5. pp. 1857-1867.

BibTeX

@article{38d88747ae27460e9516d42697b953aa,

title = "Hyperbolic 2-spheres with conical singularities, accessory parameters and K{\"a}hler metrics on M0,n",

abstract = "We show that the real-valued function Sα on the moduli space M0,n of pointed rational curves, defined as the critical value of the Liouville action functional on a hyperbolic 2-sphere with n ≥ 3 conical singularities of arbitrary orders α = {α1,..., αn}, generates accessory parameters of the associated Fuchsian differential equation as their common antiderivative. We introduce a family of K{\"a}hler metrics on M0,n parameterized by the set of orders a, explicitly relate accessory parameters to these metrics, and prove that the functions Sα are their K{\"a}hler potentials.",

keywords = "Accessory parameters, Fuchsian differential equations, Liouville action, Weil-Petersson metric",

author = "Leon Takhtajan and Peter Zograf",

year = "2003",

month = may,

day = "1",

doi = "10.1090/S0002-9947-02-03243-9",

language = "English",

volume = "355",

pages = "1857--1867",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

number = "5",

}

RIS

TY - JOUR

T1 - Hyperbolic 2-spheres with conical singularities, accessory parameters and Kähler metrics on M0,n

AU - Takhtajan, Leon

AU - Zograf, Peter

PY - 2003/5/1

Y1 - 2003/5/1

N2 - We show that the real-valued function Sα on the moduli space M0,n of pointed rational curves, defined as the critical value of the Liouville action functional on a hyperbolic 2-sphere with n ≥ 3 conical singularities of arbitrary orders α = {α1,..., αn}, generates accessory parameters of the associated Fuchsian differential equation as their common antiderivative. We introduce a family of Kähler metrics on M0,n parameterized by the set of orders a, explicitly relate accessory parameters to these metrics, and prove that the functions Sα are their Kähler potentials.

AB - We show that the real-valued function Sα on the moduli space M0,n of pointed rational curves, defined as the critical value of the Liouville action functional on a hyperbolic 2-sphere with n ≥ 3 conical singularities of arbitrary orders α = {α1,..., αn}, generates accessory parameters of the associated Fuchsian differential equation as their common antiderivative. We introduce a family of Kähler metrics on M0,n parameterized by the set of orders a, explicitly relate accessory parameters to these metrics, and prove that the functions Sα are their Kähler potentials.

KW - Accessory parameters

KW - Fuchsian differential equations

KW - Liouville action

KW - Weil-Petersson metric

UR - http://www.scopus.com/inward/record.url?scp=0037408043&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-02-03243-9

DO - 10.1090/S0002-9947-02-03243-9

M3 - Article

AN - SCOPUS:0037408043

VL - 355

SP - 1857

EP - 1867

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 5

ER -

ID: 127186885