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RECURSION FOR MASUR-VEECH VOLUMES OF MODULI SPACES OF QUADRATIC DIFFERENTIALS
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- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 21 / Issue 4 / July 2022
- Published online by Cambridge University Press:
- 08 January 2021, pp. 1471-1476
- Print publication:
- July 2022
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We derive a quadratic recursion relation for the linear Hodge integrals of the form
$\langle \tau _{2}^{n}\lambda _{k}\rangle $
. These numbers are used in a formula for Masur-Veech volumes of moduli spaces of quadratic differentials discovered by Chen, Möller and Sauvaget. Therefore, our recursion provides an efficient way of computing these volumes.
Darboux Transformations for the KP Hierarchy in the Segal-Wilson Setting
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- Journal:
- Canadian Journal of Mathematics / Volume 53 / Issue 2 / 01 April 2001
- Published online by Cambridge University Press:
- 20 November 2018, pp. 278-309
- Print publication:
- 01 April 2001
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- Article
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In this paper it is shown that inclusions inside the Segal-Wilson Grassmannian give rise to Darboux transformations between the solutions of the
$\text{KP}$ hierarchy corresponding to these planes. We present a closed form of the operators that procure the transformation and express them in the related geometric data. Further the associated transformation on the level of 
$\tau $-functions is given.
