2026-09-23T18:52:14Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/121490 2023-12-13 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Katz, Sheldon Duursma, Iwan Pascaleff, James Dodd, Christopher 2023-08 application/pdf en text Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-12-04 without embargo terms The student, Sungwoo Nam, accepted the attached license on 2023-07-10 at 12:54. The student, Sungwoo Nam, submitted this Dissertation for approval on 2023-07-10 at 13:00. This Dissertation was approved for publication on 2023-07-11 at 16:08. DSpace SAF Submission Ingestion Package generated from Vireo submission #19597 on 2023-12-04 at 17:01:32 eng https://hdl.handle.net/2142/121490 Copyright 2023 Sungwoo Nam Local enumerative invariants of some Gorenstein surfaces and orbifolds Nam, Sungwoo 2023-07-11 Local Gromov-witten Theory Local Gopakumar-vafa Theory Simple Normal Crossing Surfaces Del Pezzo Surfaces Shrinkable Surfaces Root Stacks Moduli Space Of Stable Sheaves On Root Stacks In this thesis, we study questions from enumerative geometry of local surfaces. We give a definition for local Gromov–Witten and local Gopakumar–Vafa invariants for some singular surfaces as a generalization of the local theory of smooth del Pezzo surfaces. The singular surfaces we consider are motivated by the physics of 5d SCFTs. We also discuss the solution to the embeddability question of these surfaces. Unlike smooth surfaces, it is a subtle question to ask whether a surface S can be embedded into a smooth Calabi–Yau 3-fold. As a technical tool, we review the theory of root stacks and toric diagrams which give a Calabi–Yau 3-fold. The construction using root stacks leads to the local theory of root stacks. The motivation for this direction is provided from the crepant resolution conjecture. We also study the Hilbert scheme of 0-dimensional substacks on a root stack of a surface along a smooth divisor and compute its topological Euler characteristic. Text Ph.D. Dissertation Mathematics University of Illinois at Urbana-Champaign Mathematics