TY  - GEN
N2  - 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.
AV  - public
CY  - Heidelberg
KW  - Enumerative Geometrie
KW  -  Integrable Systeme
KW  -  Bethe Ansatz
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/37102/
ID  - heidok37102
A1  - Schimpf, Maximilian
TI  - On the enumerative geometry of local curves
Y1  - 2025///
ER  -