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June, 2021 Sheaf Theoretic Compactifications of the Space of Rational Quartic Plane Curves
Kiryong Chung
Author Affiliations +
Taiwanese J. Math. 25(3): 463-476 (June, 2021). DOI: 10.11650/tjm/210103

Abstract

Let $R_4$ be the space of rational plane curves of degree $4$. In this paper, we obtain a sheaf theoretic compactification of $R_4$ via the space of $\alpha$-semistable pairs on $\mathbb{P}^2$ and its birational relations through wall-crossings of semistable pairs. We obtain the Poincaré polynomial of the compactified space.

Funding Statement

Kiryong Chung is partially supported by Korea NRF grant 2019R1F1A1042516.

Acknowledgments

The author would like to thank Dawei Chen for suggesting this topic and Jinhyung Park for helpful discussions and comments.

Citation

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Kiryong Chung. "Sheaf Theoretic Compactifications of the Space of Rational Quartic Plane Curves." Taiwanese J. Math. 25 (3) 463 - 476, June, 2021. https://doi.org/10.11650/tjm/210103

Information

Received: 6 August 2020; Revised: 16 December 2020; Accepted: 11 January 2021; Published: June, 2021
First available in Project Euclid: 15 January 2021

Digital Object Identifier: 10.11650/tjm/210103

Subjects:
Primary: 14E05, 14E15, 14M15

Rights: Copyright © 2021 The Mathematical Society of the Republic of China

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Vol.25 • No. 3 • June, 2021
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