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oai:www.repository.cam.ac.uk:1810/4028542026-05-23T01:40:39Zcom_1810_213747com_1810_256064col_1810_213748

Topology and combinatorics of low genus mapping spaces to projective space https://doi.org/10.17863/CAM.130075 Song, Dekun Ranganathan, Dhruv This thesis studies the topological invariants and boundary combinatorics of two classes of moduli spaces parametrising maps from elliptic curves to projective space - the Vakil--Zinger space and Kontsevich stable map spaces - combining the techniques of mixed Hodge structures, tropical moduli spaces, symmetric functions, and the Grothendieck ring of varieties. The results of the thesis extend the structures and results on the moduli spaces of low genus stable curves and genus zero stable maps to projective space, overcoming the subtlety caused by smoothability, and point the way towards higher genus generalisations. University of Cambridge 2026-03-05 Thesis Doctoral Doctor of Philosophy (PhD) eng Cambridge Trust International Scholarship, Trinity College, DPMMS https://www.repository.cam.ac.uk/handle/1810/402854 https://www.repository.cam.ac.uk/bitstreams/3e123881-f808-46ba-b213-a1795d787a16/download eaac28cd894302eef8962d7b95a4ae76 https://www.repository.cam.ac.uk/bitstreams/e22575aa-7dbc-49fe-9eba-0d63748ecd5d/download 87eda9de84448d1f82354d60eee3eb5f https://creativecommons.org/licenses/by/4.0/ Moduli space Boundary complex Symmetric function Mixed Hodge structure