On birational geometry of the space of parametrized rational curves in grassmannians

Atsushi Ito

doi:10.1090/tran/6840

On birational geometry of the space of parametrized rational curves in grassmannians

Atsushi Ito

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

1 Citation (Scopus)

Abstract

In this paper, we study the birational geometry of the Quot schemes of trivial bundles on ℙ¹ by constructing small ℚ-factorial modifica- tions of the Quot schemes as suitable moduli spaces. We determine all the models which appear in the minimal model program on the Quot schemes. As a corollary, we show that the Quot schemes are Mori dream spaces and log Fano.

Original language	English
Pages (from-to)	6279-6301
Number of pages	23
Journal	Transactions of the American Mathematical Society
Volume	369
Issue number	9
DOIs	https://doi.org/10.1090/tran/6840
Publication status	Published - 2017
Externally published	Yes

Keywords

Mori dream space
Quot scheme
Small ℚ-factorial modification

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/tran/6840

Cite this

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title = "On birational geometry of the space of parametrized rational curves in grassmannians",

abstract = "In this paper, we study the birational geometry of the Quot schemes of trivial bundles on ℙ1 by constructing small ℚ-factorial modifica- tions of the Quot schemes as suitable moduli spaces. We determine all the models which appear in the minimal model program on the Quot schemes. As a corollary, we show that the Quot schemes are Mori dream spaces and log Fano.",

keywords = "Mori dream space, Quot scheme, Small ℚ-factorial modification",

author = "Atsushi Ito",

note = "Funding Information: The author would like to express his gratitude to Professors Yoshinori Gongyo, Yujiro Kawamata, and Yasunari Nagai for valuable comments and advice. The author was supported by JSPS KAKENHI Grant No. 261881. Publisher Copyright: {\textcopyright} 2017 American Mathematical Society.",

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AU - Ito, Atsushi

N1 - Funding Information: The author would like to express his gratitude to Professors Yoshinori Gongyo, Yujiro Kawamata, and Yasunari Nagai for valuable comments and advice. The author was supported by JSPS KAKENHI Grant No. 261881. Publisher Copyright: © 2017 American Mathematical Society.

PY - 2017

Y1 - 2017

N2 - In this paper, we study the birational geometry of the Quot schemes of trivial bundles on ℙ1 by constructing small ℚ-factorial modifica- tions of the Quot schemes as suitable moduli spaces. We determine all the models which appear in the minimal model program on the Quot schemes. As a corollary, we show that the Quot schemes are Mori dream spaces and log Fano.

AB - In this paper, we study the birational geometry of the Quot schemes of trivial bundles on ℙ1 by constructing small ℚ-factorial modifica- tions of the Quot schemes as suitable moduli spaces. We determine all the models which appear in the minimal model program on the Quot schemes. As a corollary, we show that the Quot schemes are Mori dream spaces and log Fano.

KW - Mori dream space

KW - Quot scheme

KW - Small ℚ-factorial modification

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 9

ER -

On birational geometry of the space of parametrized rational curves in grassmannians

Abstract

Keywords

ASJC Scopus subject areas

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