eprintid: 37102
rev_number: 13
eprint_status: archive
userid: 9217
dir: disk0/00/03/71/02
datestamp: 2025-08-08 10:17:37
lastmod: 2025-08-11 18:03:50
status_changed: 2025-08-08 10:17:37
type: doctoralThesis
metadata_visibility: show
creators_name: Schimpf, Maximilian
title: On the enumerative geometry of local curves
subjects: ddc-510
divisions: i-110400
adv_faculty: af-11
keywords: Enumerative Geometrie, Integrable Systeme, Bethe Ansatz
abstract: This thesis studies the Gromov-Witten and stable pair invariants of local
curves. In particular, we give a closed formula for the full descendent stable
pair theory of all (non-relative) local curves in terms of the Bethe roots of
the quantum intermediate long wave system. In the process, we derive a
new explicit description of these Bethe roots, which may be of independent
interest. We further deduce rationality, functional equation and a pole restriction for the descendent stable pair theory of local curves as conjectured
by Pandharipande and Pixton. Furthermore, we show how the Bethe roots
can be used to diagonalize the descedent invariants of the tube and give
explicit formulas for the first few descendents. On the Gromov-Witten side,
we conjecture that the Gromov-Witten theory of the local elliptic curve is
governed by quasi-Jacobi forms. Finally, we compute an infinite series of
special cases, which provides evidence for our conjecture.
date: 2025
id_scheme: DOI
id_number: 10.11588/heidok.00037102
ppn_swb: 1932969071
own_urn: urn:nbn:de:bsz:16-heidok-371022
date_accepted: 2025-07-28
advisor: HASH(0x55602642da98)
language: eng
bibsort: SCHIMPFMAXONTHEENUME20250806
full_text_status: public
place_of_pub: Heidelberg
citation:   Schimpf, Maximilian  (2025) On the enumerative geometry of local curves.  [Dissertation]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/37102/1/PhDthesis.pdf