13 citations · 14 across the 6 of their papers we have counts for
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The Enumerative Geometry and Arithmetic of Banana Nano-Manifolds
Jim Bryan, Stephen Pietromonaco
A banana manifold is a Calabi-Yau threefold fibered by Abelian surfaces whose singular fibers contain banana configurations: three rational curves meeting each other in two points.…
Counting Invariant Curves: a theory of Gopakumar-Vafa invariants for Calabi-Yau threefolds with an involution
Jim Bryan, Stephen Pietromonaco
We develop a theory of Gopakumar-Vafa (GV) invariants for a Calabi-Yau threefold (CY3) which is equipped with an involution preserving the holomorphic volume form. We…
-invariant Hilbert Schemes on Abelian Surfaces and Enumerative Geometry of the Orbifold Kummer Surface
Stephen Pietromonaco
For an Abelian surface with a symplectic action by a finite group , one can define the partition function for -invariant Hilbert schemes \[Z_{A, G}(q) = \sum_{d=0}^{\inft…
An Introduction to Modern Enumerative Geometry with Applications to the Banana Manifold
Stephen Pietromonaco
The banana manifold is a smooth projective Calabi-Yau threefold fibered over by abelian surfaces. Each singular fiber contains a "banana configura…