Zobrazeno 1 - 10
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pro vyhledávání: '"Oberdieck, P"'
Autor:
Oberdieck, Georg
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 Toda. Motivated by our results we conjecture a formula for the perverse
Externí odkaz:
http://arxiv.org/abs/2408.02616
Autor:
Oberdieck, Georg
We conjecture an explicit formula for the $K$-theoretically refined Vafa-Witten invariants of the Enriques surface. By a wall-crossing argument the conjecture is equivalent to a new conjectural formula for the K-theoretically refined Pandharipande-Th
Externí odkaz:
http://arxiv.org/abs/2407.21318
Autor:
Oberdieck, Georg, Pixton, Aaron
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 induced fibration $S^{[n]} \to \Sigma^{[n]}$. The formula is expresse
Externí odkaz:
http://arxiv.org/abs/2312.13188
Autor:
Oberdieck, Georg, Schimpf, Maximilian
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 invariants of $X$ are quasi-Jacobi forms and satisfy two holomorphic an
Externí odkaz:
http://arxiv.org/abs/2308.09652
Autor:
Oberdieck, Georg
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 the Bryan-Leung formula. We also prove a new recursion that allows to
Externí odkaz:
http://arxiv.org/abs/2308.09074
Autor:
Oberdieck, Georg
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 generating series of genus $1$ invariants of the Enriques surface is the
Externí odkaz:
http://arxiv.org/abs/2305.11115
Autor:
Oberdieck, Georg
Jieao Song recently conjectured a formula for the class of a Lagrangian plane on a hyperk\"ahler variety of $K3^{[n]}$-type in terms of the class of a line on it. We give a proof of this conjecture if the line class is primitive.
Comment: 18 pag
Comment: 18 pag
Externí odkaz:
http://arxiv.org/abs/2206.10288
Autor:
Oberdieck, Georg
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 equation. We prove the conjecture in genus $0$ and for at most $3$ mark
Externí odkaz:
http://arxiv.org/abs/2202.03361
Publikováno v:
Adv. Math. 408 (2022) 108605
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 Gromov-Witten theory. When $X$ is holomorphic symplectic, Gromov-Witten invariants vanish an
Externí odkaz:
http://arxiv.org/abs/2201.11540
Publikováno v:
Comm. Math. Phys. 405 (2024), no. 26
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 BPS counts of Gopakumar and Vafa for Calabi-Yau 3-folds, Klemm and Pa
Externí odkaz:
http://arxiv.org/abs/2201.10878