Generalized symplecitc log Calabi-Yau divisors
2022-03
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Generalized symplecitc log Calabi-Yau divisors
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2022-03
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We study the symplectic divisors corresponding to the Hamiltonian circle actions on symplectic surfaces. Li-Min-Ning showed that counting toric actions on a fixed symplectic rational surface is equivalent to counting toric log Calabi-Yau divisors. Inspired by a formula by Holm-Kessler, we introduce generalized symplectic log Calabi-Yau divisors on symplectic irrationalruled surfaces. Using the language of marked divisors we prove a version of Torelli theorem, stating that the symplectic deformation classes of these divisors (with a few extra conditions) are determined by their homological information. We show that there is an one-to-one correspondence between Hamiltonian circle actions and S1-generalied symplectic log Calabi-Yau divisors in a fixed symplectic irrational ruled surface. As an application, we give a new proof of the finiteness of inequivalent Hamiltonian circle actions.
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University of Minnesota Ph.D. dissertation.June 2022. Major: Mathematics. Advisor: Tianjun Li. 1 computer file (PDF); vi, 45 pages.
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Ouyang, Liya. (2022). Generalized symplecitc log Calabi-Yau divisors. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/241606.
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