(-2)-shifted symplectic virtual cycles

Appears in collection : 2023 - T2 - WS2 - Higher structures in enumerative geometry

Behrend-Fantechi and Li-Tian showed how to produce a virtual cycle from a 2-term obstruction theory (or, in higher language, a quasi-smooth derived scheme). I will describe joint work with Jeongseok Oh that produces a virtual cycle from a 3-term symmetric obstruction theory (or, in higher language, a (-2)-shifted symplectic derived scheme). There is also a localisation formula, a K-theoretic refinement, a virtual GRR formula, etc. Earlier Borisov-Joyce used real derived differential geometry to define a real virtual homology class. When their virtual dimension is even we show our class reproduces theirs; when it is odd we show their class is torsion.

Information about the video

Date of recording 16/06/2023
Date of publication 11/04/2024
Institution IHP
Licence CC BY-NC-ND
Language English
Audience Researchers, Graduate Students
Director(s) Alexandre Duplessis
Format MP4
Venue IHP - Hermite Amphitheater

Citation data

DOI 10.57987/IHP.2023.T2.WS2.017
Cite this video THOMAS, Richard (16/06/2023). (-2)-shifted symplectic virtual cycles. IHP. Audiovisual resource. DOI: 10.57987/IHP.2023.T2.WS2.017
URL https://dx.doi.org/10.57987/IHP.2023.T2.WS2.017

Domain(s)

Algebraic Geometry

Bibliography

Counting sheaves on Calabi-Yau 4-folds, I, Duke Math Jour. 172, 1333-1409, 2023. Complex Kuranishi structures and counting sheaves on Calabi-Yau 4-folds, II. arXiv:2305.16441