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 …
theory of the Calabi–Yau threefold S * ES× E for all curve classes which are primitive in the …
Curve counting on abelian surfaces and threefolds
We study the enumerative geometry of algebraic curves on abelian surfaces and threefolds.
In the abelian surface case, the theory is parallel to the well-developed study of the reduced …
In the abelian surface case, the theory is parallel to the well-developed study of the reduced …
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 …
Sheaf counting on local K3 surfaces
D Maulik, RP Thomas - arXiv preprint arXiv:1806.02657, 2018 - arxiv.org
There are two natural ways to count stable pairs or Joyce-Song pairs on $ X=\mathrm
{K3}\times\mathbb C $; one via weighted Euler characteristic and the other by virtual …
{K3}\times\mathbb C $; one via weighted Euler characteristic and the other by virtual …
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 …
Algebraicity and smoothness of fixed point stacks
M Romagny - arXiv preprint arXiv:2205.11114, 2022 - arxiv.org
We study algebraicity and smoothness of fixed point stacks for flat group schemes which
have a finite composition series whose factors are either reductive or proper, flat, finitely …
have a finite composition series whose factors are either reductive or proper, flat, finitely …
Enumerative mirror symmetry for moduli spaces of Higgs bundles and S-duality
D Nesterov - arXiv preprint arXiv:2302.08379, 2023 - arxiv.org
We derive conjectures, called genus 1 Enumerative mirror symmetry for moduli spaces of
Higgs bundles, which relate curve-counting invariants of moduli spaces of Higgs $\mathrm …
Higgs bundles, which relate curve-counting invariants of moduli spaces of Higgs $\mathrm …
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 …
which acts symplectically on the K3 surface and acts by shifting by an $ N $-torsion point on …
Donaldson-Thomas invariants of abelian threefolds and Bridgeland stability conditions
G Oberdieck, D Piyaratne, Y Toda - arXiv preprint arXiv:1808.02735, 2018 - arxiv.org
We study the reduced Donaldson-Thomas theory of abelian threefolds using Bridgeland
stability conditions. The main result is the invariance of the reduced Donaldson-Thomas …
stability conditions. The main result is the invariance of the reduced Donaldson-Thomas …