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 …
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 …
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 …
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 …
$(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 …
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 …
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 …
correspondence, with descendants, and study the behaviour of the correspondence under …
Gromov–Witten theory of complete intersections via nodal invariants
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 …
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 $-relative generating series of Pandharipande-Thomas …
0$. 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 …
ON HilbSym CORRESPONDENCE FOR K3 SURFACES DENIZ GENLIK AND HSIAN-HUA …