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GIT quotient of holomorphic foliations on ℂℙ2 of degree 2 and quartic plane curves

  • Claudia R. Alcántara EMAIL logo and Juan Vásquez Aquino
Published/Copyright: August 5, 2024

Abstract

We study the quotient variety of the space of foliations on 2 of degree 2 up to change of coordinates. We find the intersection Betti numbers of this variety. As a corollary, we have that these intersection Betti numbers coincide with the intersection Betti numbers of the quotient variety of quartic plane curves. Finally, we give an explicit isomorphism between the space of foliations of degree 2 with different singular points, without invariant lines and the space of smooth quartic plane curves.


Communicated by Shigeharu Takayama


Funding source: Conachyt

Award Identifier / Grant number: 284424

Funding statement: This work was supported by the CONACHyT under Grant 284424. The second author is supported with a postdoc position by CONAHCyT.

Acknowledgements

The authors would like to thank the referee for the valuable contributions that significantly improved the article.

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Received: 2024-01-21
Revised: 2024-05-17
Published Online: 2024-08-05
Published in Print: 2025-06-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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