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 …

Curve counting on the Enriques surface and the Klemm-Mari\~{n} o formula

G Oberdieck - arXiv preprint arXiv:2305.11115, 2023 - arxiv.org
We determine the Gromov-Witten invariants of the local Enriques surfaces for all genera and
curve classes and prove the Klemm-Mari\~{n} o formula. In particular, we show that the …

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 …

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 …

Quasimaps to moduli spaces of sheaves on a surface

D Nesterov - Forum of Mathematics, Sigma, 2024 - cambridge.org
In this article, we study quasimaps to moduli spaces of sheaves on a $ K3 $ surface S. We
construct a surjective cosection of the obstruction theory of moduli spaces of $\epsilon …

Quantum cohomology of the Hilbert scheme of points on an elliptic surface

G Oberdieck, A Pixton - arXiv preprint arXiv:2312.13188, 2023 - arxiv.org
We determine the quantum multiplication with divisor classes on the Hilbert scheme of
points on an elliptic surface $ S\to\Sigma $ for all curve classes which are contracted by the …

Logarithmic enumerative geometry for curves and sheaves

D Maulik, D Ranganathan - arXiv preprint arXiv:2311.14150, 2023 - arxiv.org
We propose a logarithmic enhancement of the Gromov-Witten/Donaldson-Thomas
correspondence, with descendants, and study the behaviour of the correspondence under …

Gromov–Witten theory of complete intersections via nodal invariants

H Argüz, P Bousseau, R Pandharipande… - Journal of …, 2023 - Wiley Online Library
We provide an inductive algorithm computing Gromov–Witten invariants in all genera with
arbitrary insertions of all smooth complete intersections in projective space. We also prove …

Pandharipande-Thomas theory of elliptic threefolds, quasi-Jacobi forms and holomorphic anomaly equations

G Oberdieck, M Schimpf - arXiv preprint arXiv:2308.09652, 2023 - arxiv.org
Let $\pi: X\to B $ be an elliptically fibered threefold satisfying $ c_3 (T_X\otimes\omega_X)=
0$. We conjecture that the $\pi $-relative generating series of Pandharipande-Thomas …

[PDF][PDF] On Hilb/Sym correspondence for K3 surfaces

D Genlik, HH Tseng - arXiv preprint arXiv:2304.06536, 2023 - arxiv.org
arXiv:2304.06536v1 [math.AG] 13 Apr 2023 Page 1 arXiv:2304.06536v1 [math.AG] 13 Apr 2023
ON HilbSym CORRESPONDENCE FOR K3 SURFACES DENIZ GENLIK AND HSIAN-HUA …