Algebraic Montgomery-Yang problem and smooth obstructions
| Autor: | Jo, Woohyeok, Park, Jongil, Park, Kyungbae |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $S$ be a rational homology complex projective plane with quotient singularities. The algebraic Montgomery-Yang problem conjectures that the number of singular points of $S$ is at most three if its smooth locus is simply-connected. In this paper, we leverage results from the study of smooth 4-manifolds, including the Donaldson diagonalization theorem and Heegaard Floer correction terms, to establish additional conditions for $S$. As a result, we eliminate the possibility of a rational homology complex projective plane of specific types with four singularities. Moreover, we identify large families encompassing infinitely many types of singularities that satisfy the orbifold BMY inequality, a key property in algebraic geometry, yet are obstructed from being a rational homology complex projective plane due to smooth conditions. Additionally, we discuss computational results related to this problem, offering new insights into the algebraic Montgomery-Yang problem. Comment: 26 pages, 14 figures, minor revisions for the purpose of correcting typos and refining the language |
| Databáze: | arXiv |
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