ALGEBRAIC GEOMETRY SEMINAR & TRINO - Tuesday 17 October, at 15:00 - Georg Oberdieck - Venue: Luigi Stasi Seminar room

[ICTP Math Section]

ALGEBRAIC GEOMETRY SEMINAR & TRINO on "Curve counting on the Enriques 
surface and orthogonal modular forms"

Tuesday 17 Oct 2023, from 15:00 to 16:30

Venue: ICTP Leonardo Building - Luigi Stasi Seminar Room


Speaker: Georg Oberdieck (KTH Royal Institute of Technology, Stockholm)


Abstract: An Enriques surface is the quotient of a K3 surface by a 
fixed-point free involution. Klemm and Marino conjectured that the 
Gromov-Witten invariants (which are virtual counts of curves) of the 
local Enriques surface are certain orthogonal modular forms. In 
particular the genus 1 series recovers Borcherds famous automorphic form 
on the moduli space of Enriques surface. However, not much is known 
about the more general descendent Gromov-Witten theory of the Enriques 
surface. In this talk I will first discuss and sketch the proof of the 
Klemm-Marino formula and then explain a conjecture which links the 
descendent Gromov-Witten invariants of the Enriques to orthogonal 
modular forms in general. If time permits I will give some explicit 
formulas for point constraints and their descendents.

https://indico.ictp.it/event/10558/

/Additional information can be found on Trino website:
https://sites.google.com/view/trinotriestino/home/



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