Pathologies of the Hilbert scheme of points of a supersingular Enriques surface

T.K. Srivastava, Bulletin Des Sciences Mathematiques 167 (2021).


Journal Article | Published | English

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Abstract
We show that Hilbert schemes of points on supersingular Enriques surface in characteristic 2, Hilbn(X), for n ≥ 2 are simply connected, symplectic varieties but are not irreducible symplectic as the hodge number h2,0 > 1, even though a supersingular Enriques surface is an irreducible symplectic variety. These are the classes of varieties which appear only in characteristic 2 and they show that the hodge number formula for G¨ottsche-Soergel does not hold over haracteristic 2. It also gives examples of varieties with trivial canonical class which are neither irreducible symplectic nor Calabi-Yau, thereby showing that there are strictly more classes of simply connected varieties with trivial canonical class in characteristic 2 than over C as given by Beauville-Bogolomov decomposition theorem.
Publishing Year
Date Published
2021-03-01
Journal Title
Bulletin des Sciences Mathematiques
Acknowledgement
I would like to thank M. Zdanwociz for various mathematical discussions which lead to this article, Tamas Hausel for hosting me in his research group at IST Austria and the anonymous referee for their helpful suggestions and comments. This research has received funding from the European Union's Horizon 2020 Marie Sklodowska-Curie Actions Grant No. 754411 and Institue of Science and Technology Austria IST-PLUS Grant No. 754411.
Volume
167
Issue
03
Article Number
102957
ISSN
IST-REx-ID

Cite this

Srivastava TK. Pathologies of the Hilbert scheme of points of a supersingular Enriques surface. Bulletin des Sciences Mathematiques. 2021;167(03). doi:10.1016/j.bulsci.2021.102957
Srivastava, T. K. (2021). Pathologies of the Hilbert scheme of points of a supersingular Enriques surface. Bulletin Des Sciences Mathematiques. Elsevier. https://doi.org/10.1016/j.bulsci.2021.102957
Srivastava, Tanya K. “Pathologies of the Hilbert Scheme of Points of a Supersingular Enriques Surface.” Bulletin Des Sciences Mathematiques. Elsevier, 2021. https://doi.org/10.1016/j.bulsci.2021.102957.
T. K. Srivastava, “Pathologies of the Hilbert scheme of points of a supersingular Enriques surface,” Bulletin des Sciences Mathematiques, vol. 167, no. 03. Elsevier, 2021.
Srivastava TK. 2021. Pathologies of the Hilbert scheme of points of a supersingular Enriques surface. Bulletin des Sciences Mathematiques. 167(03), 102957.
Srivastava, Tanya K. “Pathologies of the Hilbert Scheme of Points of a Supersingular Enriques Surface.” Bulletin Des Sciences Mathematiques, vol. 167, no. 03, 102957, Elsevier, 2021, doi:10.1016/j.bulsci.2021.102957.
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