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Filtered geometric lattices and Lefschet...

Adiprasito, Karim Al...

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Filtered geometric lattices and Lefschetz Section Theorems over the tropical semiring by Adiprasito, Karim Alexander ( Author )

Content Provider	Lemonjar Open Access
Publisher	Australian National University
Publication Date	04-08-2023
Summary	The purpose of this paper is to establish analogues of the classical Lefschetz Section Theorem for smooth tropical varieties. More precisely, we prove tropical analogues of the section theorems of Lefschetz, Andreotti-Frankel, Bott-Milnor-Thom, Hamm-L\^e and Kodaira-Spencer, and the vanishing theorems of Andreotti-Frankel and Akizuki-Kodaira-Nakano. We start the paper by resolving a conjecture of Mikhalkin and Ziegler (2008) concerning the homotopy types of certain filtrations of geometric lattices, generalizing several known properties of full geometric lattices. This translates to a crucial index estimate for the stratified Morse data at critical points of the tropical variety; it can also by itself be interpreted as a Lefschetz-type theorem for matroids.
ISBN	-
Item Type	Article
File Type	pdf
File Size	29.34 KB
Language	English
Subjects	-
Unlimited	MYR 0.01
Total read	-
URL	http://arxiv.org/abs/1401.7301

Citation

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AMA 11th EditionReferences

Adiprasito, Karim Alexander. Filtered geometric lattices and Lefschetz Section Theorems over the tropical semiring. Australian National University. August 04, 2023. Accessed June 13, 2025. https://online.provdatabase.com/cite/10820

APA 7th EditionReferences

Adiprasito, Karim Alexander. (2023). Filtered geometric lattices and Lefschetz Section Theorems over the tropical semiring. Australian National University. https://online.provdatabase.com/cite/10820

Chicago 17th EditionReferences

Adiprasito, Karim Alexander. Filtered geometric lattices and Lefschetz Section Theorems over the tropical semiring. Australian National University. 2023. https://online.provdatabase.com/cite/10820

HarvardReferences

Adiprasito, Karim Alexander. (2023). Filtered geometric lattices and Lefschetz Section Theorems over the tropical semiring. [Online]. Australian National University. Available from: https://online.provdatabase.com/cite/10820. (Accessed 13 June 2025).

Harvard AustraliaReferences

Adiprasito, Karim Alexander, 2023, Filtered geometric lattices and Lefschetz Section Theorems over the tropical semiring, Australian National University, viewed 13 June 2025, <https://online.provdatabase.com/cite/10820>

MLA 9th EditionWorks Cited

Adiprasito, Karim Alexander. Filtered geometric lattices and Lefschetz Section Theorems over the tropical semiring. Australian National University, 2023. PROV Database, https://online.provdatabase.com/cite/10820.

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