Integration over tropical plane curves and ultradiscretization

Shinsuke Iwao

doi:10.1093/imrn/rnp129

Integration over tropical plane curves and ultradiscretization

Shinsuke Iwao

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

In this article we study holomorphic integrals on tropical plane curves in view of ultradiscretization. We prove that the lattice integrals over tropical curves can be obtained as a certain limit of complex integrals over Riemann surfaces.

Original language	English
Pages (from-to)	112-148
Number of pages	37
Journal	International Mathematics Research Notices
Volume	2010
Issue number	1
DOIs	https://doi.org/10.1093/imrn/rnp129
Publication status	Published - 2010
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

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10.1093/imrn/rnp129

Cite this

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title = "Integration over tropical plane curves and ultradiscretization",

abstract = "In this article we study holomorphic integrals on tropical plane curves in view of ultradiscretization. We prove that the lattice integrals over tropical curves can be obtained as a certain limit of complex integrals over Riemann surfaces.",

author = "Shinsuke Iwao",

note = "Funding Information: I am very grateful to Professor Tetsuji Tokihiro and Professor Ralph Willox for helpful comments on this article. I would like to thank Professor Jonathan Nimmo for valuable advice on the revised version of this article. This work was supported by grant-in-aid from the Japan Society for the Promotion of Science Fellows [21-7090].",

year = "2010",

doi = "10.1093/imrn/rnp129",

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N1 - Funding Information: I am very grateful to Professor Tetsuji Tokihiro and Professor Ralph Willox for helpful comments on this article. I would like to thank Professor Jonathan Nimmo for valuable advice on the revised version of this article. This work was supported by grant-in-aid from the Japan Society for the Promotion of Science Fellows [21-7090].

PY - 2010

Y1 - 2010

N2 - In this article we study holomorphic integrals on tropical plane curves in view of ultradiscretization. We prove that the lattice integrals over tropical curves can be obtained as a certain limit of complex integrals over Riemann surfaces.

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DO - 10.1093/imrn/rnp129

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JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

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Integration over tropical plane curves and ultradiscretization

Abstract

ASJC Scopus subject areas

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