Gromov-Witten Theory of Hilb(K3,n), Modular forms and K3 x E.
Event details
| Date | 20.10.2014 |
| Hour | 15:15 › 17:00 |
| Speaker | Georg Oberdieck (ETHZ) |
| Location | |
| Category | Conferences - Seminars |
One of the main tools in the proof of the Stable Pairs / Gromov-Witten correspondence for toric Calabi-Yau threefolds is a correspondence between the relative GW theory of P1 x S and the genus 0 GW theory of Hilb(S,n), where S is the two-dimensional affine plane and Hilb(S,n) is its Hilbert scheme of points. A natural and open question is if such a correspondence exist for other, in particular compact, surfaces S as well.
In this talk, we will consider this question in the case where S is a K3 surface. First, i will first present recent results on the genus 0 GW theory of Hilb(S,n) the Hilbert scheme of points of S. These results lead to conjectures about the full genus 0 GW theory of Hilb(S,n) (in the primitive case).
Second, i will explain a conjecture that a correspondence to P1 x S should exist and state its particular form. As an outcome, we obtain predictions for the GW Theory of K3xE in terms of a Siegel modular form, the Igusa cusp form. The second part is joint work with R. Pandharipande.
In this talk, we will consider this question in the case where S is a K3 surface. First, i will first present recent results on the genus 0 GW theory of Hilb(S,n) the Hilbert scheme of points of S. These results lead to conjectures about the full genus 0 GW theory of Hilb(S,n) (in the primitive case).
Second, i will explain a conjecture that a correspondence to P1 x S should exist and state its particular form. As an outcome, we obtain predictions for the GW Theory of K3xE in terms of a Siegel modular form, the Igusa cusp form. The second part is joint work with R. Pandharipande.
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