Gromov-Witten/Hilbert versus AdS3/CFT2 Correspondence
W Lerche - arXiv preprint arXiv:2310.15237, 2023 - arxiv.org
We consider the boundary dual of AdS3xS3xK3 for NS5-flux Q5= 1, which is described by a
sigma model with target space given by the d-fold symmetric product of K3. Building on …
sigma model with target space given by the d-fold symmetric product of K3. Building on …
Holomorphic anomaly equations for the Hilbert scheme of points of a K3 surface
G Oberdieck - Geometry & Topology, 2024 - msp.org
We conjecture that the generating series of Gromov–Witten invariants of the Hilbert schemes
of n points on a K3 surface are quasi-Jacobi forms and satisfy a holomorphic anomaly …
of n points on a K3 surface are quasi-Jacobi forms and satisfy a holomorphic anomaly …
Gopakumar–Vafa type invariants of holomorphic symplectic 4-folds
Y Cao, G Oberdieck, Y Toda - Communications in Mathematical Physics, 2024 - Springer
Abstract Using reduced Gromov–Witten theory, we define new invariants which capture the
enumerative geometry of curves on holomorphic symplectic 4-folds. The invariants are …
enumerative geometry of curves on holomorphic symplectic 4-folds. The invariants are …
Multiple cover formulas for K3 geometries, wall-crossing, and Quot schemes
G Oberdieck - arXiv preprint arXiv:2111.11239, 2021 - arxiv.org
Let $ S $ be a K3 surface. We study the reduced Donaldson-Thomas theory of the cap
$(S\times\mathbb {P}^ 1)/S_ {\infty} $ by a second cosection argument. We obtain four main …
$(S\times\mathbb {P}^ 1)/S_ {\infty} $ by a second cosection argument. We obtain four main …
Stable pairs and Gopakumar-Vafa type invariants on holomorphic symplectic 4-folds
Y Cao, G Oberdieck, Y Toda - Advances in Mathematics, 2022 - Elsevier
As an analogy to Gopakumar-Vafa conjecture on Calabi-Yau 3-folds, Klemm-
Pandharipande defined Gopakumar-Vafa type invariants of a Calabi-Yau 4-fold X using …
Pandharipande defined Gopakumar-Vafa type invariants of a Calabi-Yau 4-fold X using …
Equivariant categories of symplectic surfaces and fixed loci of Bridgeland moduli spaces
T Beckmann, G Oberdieck - arXiv preprint arXiv:2006.13899, 2020 - arxiv.org
Given an action of a finite group $ G $ on the derived category of a smooth projective variety
$ X $ we relate the fixed loci of the induced $ G $-action on moduli spaces of stable objects …
$ X $ we relate the fixed loci of the induced $ G $-action on moduli spaces of stable objects …
On the descendent Gromov-Witten theory of a K3 surface
G Oberdieck - arXiv preprint arXiv:2308.09074, 2023 - arxiv.org
We study the reduced descendent Gromov-Witten theory of K3 surfaces in primitive curve
classes. We present a conjectural closed formula for the stationary theory, which generalizes …
classes. We present a conjectural closed formula for the stationary theory, which generalizes …
Tropical curves in abelian surfaces III: pearl diagrams and multiple cover formulas
T Blomme - arXiv preprint arXiv:2205.07684, 2022 - arxiv.org
This paper is the third installment in a series of papers devoted to the computation of
enumerative invariants of abelian surfaces through the tropical approach. We develop a …
enumerative invariants of abelian surfaces through the tropical approach. We develop a …
Correlated Gromov-Witten invariants
T Blomme, F Carocci - arXiv preprint arXiv:2409.09472, 2024 - arxiv.org
We introduce a geometric refinement of Gromov-Witten invariants for $\mathbb P^ 1$-
bundles relative to the natural fiberwise boundary structure. We call these refined invariant …
bundles relative to the natural fiberwise boundary structure. We call these refined invariant …
A short proof of the multiple cover formula for point insertions
T Blomme - arXiv preprint arXiv:2501.01274, 2025 - arxiv.org
A few years ago, G. Oberdieck conjectured a multiple cover fomula that determines the
number of curves of fixed genus and degree passing through a configuration of points in an …
number of curves of fixed genus and degree passing through a configuration of points in an …