52 citations · 193 across the 37 of their papers we have counts for
39 papers
Gromov-Witten theory of abelian varieties in families and modular forms
Georg Oberdieck
This is the first paper in a series on the Gromov-Witten theory of the universal abelian variety over the moduli space of principally polarized abelian varieties of dimension .…
The multiple cover formula for and abelian surfaces
Georg Oberdieck, Rahul Pandharipande
All reduced descendent Gromov-Witten invariants of and abelian surfaces in primitive curve classes can be calculated by the methods of \cite{BOPY,MPT}. To handle the imprimiti…
IMProofBench: Benchmarking AI on Research-Level Mathematical Proof Generation
Johannes Schmitt, Gergely Bérczi, Jasper Dekoninck +57
As the mathematical capabilities of large language models (LLMs) improve, it becomes increasingly important to evaluate their performance on research-level tasks at the frontier of…
Quasi-modular forms for the orthogonal group and Gromov-Witten theory of Enriques surfaces
Georg Oberdieck, Brandon Williams
We develop the theory of almost-holomorphic and quasimodular forms for orthogonal groups of a lattice of signature through orthogonal lowering and raising operators. The in…
Towards refined curve counting on the Enriques surface II: Motivic refinements
Georg Oberdieck
We study the motivic Pandharipande-Thomas invariants of the Enriques Calabi-Yau threefolds in fiber curve classes by basic computations and analysis of a wallcrossing formula of To…
Towards refined curve counting on the Enriques surface I: K-theoretic refinements
Georg Oberdieck
We conjecture an explicit formula for the -theoretically refined Vafa-Witten invariants of the Enriques surface. By a wall-crossing argument the conjecture is equivalent to a ne…
Quantum cohomology of the Hilbert scheme of points on an elliptic surface
Georg Oberdieck, Aaron Pixton
We determine the quantum multiplication with divisor classes on the Hilbert scheme of points on an elliptic surface for all curve classes which are contracted by the indu…
Pandharipande-Thomas theory of elliptic threefolds, quasi-Jacobi forms and holomorphic anomaly equations
Georg Oberdieck, Maximilian Schimpf
Let be an elliptically fibered threefold satisfying . We conjecture that the -relative generating series of Pandharipande-Thomas invariants…
On the descendent Gromov-Witten theory of a K3 surface
Georg Oberdieck
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…
Curve counting on the Enriques surface and the Klemm-Mariño formula
Georg Oberdieck
We determine the Gromov-Witten invariants of the local Enriques surfaces for all genera and curve classes and prove the Klemm-Mariño formula. In particular, we show that the genera…
Lagrangian planes in hyperkähler varieties of -type
Georg Oberdieck
Jieao Song recently conjectured a formula for the class of a Lagrangian plane on a hyperkähler variety of -type in terms of the class of a line on it. We give a proof of…
Holomorphic anomaly equations for the Hilbert scheme of points of a K3 surface
Georg Oberdieck
We conjecture that the generating series of Gromov-Witten invariants of the Hilbert schemes of points on a K3 surface are quasi-Jacobi forms and satisfy a holomorphic anomaly e…
Gopakumar-Vafa type invariants of holomorphic symplectic 4-folds
Yalong Cao, Georg Oberdieck, Yukinobu Toda
Using reduced Gromov-Witten theory, we define new invariants which capture the enumerative geometry of curves on holomorphic symplectic 4-folds. The invariants are analogous to the…
Stable pairs and Gopakumar-Vafa type invariants on holomorphic symplectic 4-folds
Yalong Cao, Georg Oberdieck, Yukinobu Toda
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 using Gromov-Witten theory.…
Universality of Descendent Integrals over Moduli Spaces of Stable Sheaves on Surfaces
Georg Oberdieck
We interprete results of Markman on monodromy operators as a universality statement for descendent integrals over moduli spaces of stable sheaves on surfaces. This yields effe…
Marked relative invariants and GW/PT correspondences
Georg Oberdieck
We introduce marked relative Pandharipande-Thomas (PT) invariants for a pair of a smooth projective threefold and a smooth divisor. These invariants are defined by integrat…
Multiple cover formulas for K3 geometries, wall-crossing, and Quot schemes
Georg Oberdieck
Let be a K3 surface. We study the reduced Donaldson-Thomas theory of the cap by a second cosection argument. We obtain four main results:…
Hilbert schemes of K3 surfaces, generalized Kummer, and cobordism classes of hyper-Kähler manifolds
Georg Oberdieck, Jieao Song, Claire Voisin
We prove that the complex cobordism class of any hyper-Kähler manifold of dimension is a unique combination with rational coefficients of classes of products of punctual Hilbe…
Gromov-Witten theory and Noether-Lefschetz theory for holomorphic-symplectic varieties
Georg Oberdieck
We use Noether-Lefschetz theory to study the reduced Gromov--Witten invariants of a holomorphic-symplectic variety of -type. This yields strong evidence for a new conject…
Gromov-Witten theory of K3 surfaces and a Kaneko-Zagier equation for Jacobi forms
Jan-Willem van Ittersum, Georg Oberdieck, Aaron Pixton
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 u…
Equivariant categories of symplectic surfaces and fixed loci of Bridgeland moduli spaces
Thorsten Beckmann, Georg Oberdieck
Given an action of a finite group on the derived category of a smooth projective variety we relate the fixed loci of the induced -action on moduli spaces of stable objec…
On equivariant derived categories
Thorsten Beckmann, Georg Oberdieck
We study the equivariant category associated to a finite group action on the derived category of coherent sheaves of a smooth projective variety. We discuss decompositions of the e…
Motivic decompositions for the Hilbert scheme of points of a K3 surface
Andrei Neguţ, Georg Oberdieck, Qizheng Yin
We construct an explicit, multiplicative Chow-Künneth decomposition for the Hilbert scheme of points of a K3 surface. We further refine this decomposition with respect to the actio…
A Lie algebra action on the Chow ring of the Hilbert scheme of points of a K3 surface
Georg Oberdieck
We construct an action of the Neron--Severi part of the Looijenga-Lunts-Verbitsky Lie algebra on the Chow ring of the Hilbert scheme of points on a K3 surface. This yields a simpli…