Holomorphic anomaly equations and the Igusa cusp form conjecture

G Oberdieck, A Pixton - Inventiones mathematicae, 2018 - Springer
Let S be a K3 surface and let E be an elliptic curve. We solve the reduced Gromov–Witten
theory of the Calabi–Yau threefold S * ES× E for all curve classes which are primitive in the …

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 …

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 …

Gromov–Witten theory of K3 surfaces and a Kaneko–Zagier equation for Jacobi forms

JW van Ittersum, G Oberdieck, A Pixton - Selecta Mathematica, 2021 - Springer
We prove the existence of quasi-Jacobi form solutions for an analogue of the Kaneko–
Zagier differential equation for Jacobi forms. The transformation properties of the solutions …

On reduced stable pair invariants

G Oberdieck - Mathematische Zeitschrift, 2018 - Springer
Abstract Let X= S * EX= S× E be the product of a K3 surface S and an elliptic curve E.
Reduced stable pair invariants of X can be defined via (1) cutting down the reduced virtual …

Curve counting on elliptic Calabi–Yau threefolds via derived categories

G Oberdieck, J Shen - Journal of the European Mathematical Society, 2019 - ems.press
We prove the elliptic transformation law of Jacobi forms for the generating series of
Pandharipande–Thomas invariants of an elliptic Calabi–Yau threefold over a reduced class …

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 …

CHL Calabi-Yau threefolds: Curve counting, Mathieu moonshine and Siegel modular forms

J Bryan, G Oberdieck - arXiv preprint arXiv:1811.06102, 2018 - arxiv.org
A CHL model is the quotient of $\mathrm {K3}\times E $ by an order $ N $ automorphism
which acts symplectically on the K3 surface and acts by shifting by an $ N $-torsion point on …