---
_id: '9173'
abstract:
- lang: eng
  text: 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.
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.
article_number: '102957'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Tanya K
  full_name: Srivastava, Tanya K
  id: 4D046628-F248-11E8-B48F-1D18A9856A87
  last_name: Srivastava
citation:
  ama: Srivastava TK. Pathologies of the Hilbert scheme of points of a supersingular
    Enriques surface. <i>Bulletin des Sciences Mathematiques</i>. 2021;167(03). doi:<a
    href="https://doi.org/10.1016/j.bulsci.2021.102957">10.1016/j.bulsci.2021.102957</a>
  apa: Srivastava, T. K. (2021). Pathologies of the Hilbert scheme of points of a
    supersingular Enriques surface. <i>Bulletin Des Sciences Mathematiques</i>. Elsevier.
    <a href="https://doi.org/10.1016/j.bulsci.2021.102957">https://doi.org/10.1016/j.bulsci.2021.102957</a>
  chicago: Srivastava, Tanya K. “Pathologies of the Hilbert Scheme of Points of a
    Supersingular Enriques Surface.” <i>Bulletin Des Sciences Mathematiques</i>. Elsevier,
    2021. <a href="https://doi.org/10.1016/j.bulsci.2021.102957">https://doi.org/10.1016/j.bulsci.2021.102957</a>.
  ieee: T. K. Srivastava, “Pathologies of the Hilbert scheme of points of a supersingular
    Enriques surface,” <i>Bulletin des Sciences Mathematiques</i>, vol. 167, no. 03.
    Elsevier, 2021.
  ista: Srivastava TK. 2021. Pathologies of the Hilbert scheme of points of a supersingular
    Enriques surface. Bulletin des Sciences Mathematiques. 167(03), 102957.
  mla: Srivastava, Tanya K. “Pathologies of the Hilbert Scheme of Points of a Supersingular
    Enriques Surface.” <i>Bulletin Des Sciences Mathematiques</i>, vol. 167, no. 03,
    102957, Elsevier, 2021, doi:<a href="https://doi.org/10.1016/j.bulsci.2021.102957">10.1016/j.bulsci.2021.102957</a>.
  short: T.K. Srivastava, Bulletin Des Sciences Mathematiques 167 (2021).
date_created: 2021-02-21T23:01:20Z
date_published: 2021-03-01T00:00:00Z
date_updated: 2023-08-07T13:47:48Z
day: '01'
department:
- _id: TaHa
doi: 10.1016/j.bulsci.2021.102957
ec_funded: 1
external_id:
  arxiv:
  - '2010.08976'
  isi:
  - '000623881600009'
intvolume: '       167'
isi: 1
issue: '03'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2010.08976
month: '03'
oa: 1
oa_version: Preprint
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: Bulletin des Sciences Mathematiques
publication_identifier:
  issn:
  - 0007-4497
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Pathologies of the Hilbert scheme of points of a supersingular Enriques surface
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 167
year: '2021'
...
---
_id: '6835'
abstract:
- lang: eng
  text: We derive the Hasse principle and weak approximation for fibrations of certain
    varieties in the spirit of work by Colliot-Thélène–Sansuc and Harpaz–Skorobogatov–Wittenberg.
    Our varieties are defined through polynomials in many variables and part of our
    work is devoted to establishing Schinzel's hypothesis for polynomials of this
    kind. This last part is achieved by using arguments behind Birch's well-known
    result regarding the Hasse principle for complete intersections with the notable
    difference that we prove our result in 50% fewer variables than in the classical
    Birch setting. We also study the problem of square-free values of an integer polynomial
    with 66.6% fewer variables than in the Birch setting.
article_number: '102794'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Kevin N
  full_name: Destagnol, Kevin N
  id: 44DDECBC-F248-11E8-B48F-1D18A9856A87
  last_name: Destagnol
- first_name: Efthymios
  full_name: Sofos, Efthymios
  last_name: Sofos
citation:
  ama: Destagnol KN, Sofos E. Rational points and prime values of polynomials in moderately
    many variables. <i>Bulletin des Sciences Mathematiques</i>. 2019;156(11). doi:<a
    href="https://doi.org/10.1016/j.bulsci.2019.102794">10.1016/j.bulsci.2019.102794</a>
  apa: Destagnol, K. N., &#38; Sofos, E. (2019). Rational points and prime values
    of polynomials in moderately many variables. <i>Bulletin Des Sciences Mathematiques</i>.
    Elsevier. <a href="https://doi.org/10.1016/j.bulsci.2019.102794">https://doi.org/10.1016/j.bulsci.2019.102794</a>
  chicago: Destagnol, Kevin N, and Efthymios Sofos. “Rational Points and Prime Values
    of Polynomials in Moderately Many Variables.” <i>Bulletin Des Sciences Mathematiques</i>.
    Elsevier, 2019. <a href="https://doi.org/10.1016/j.bulsci.2019.102794">https://doi.org/10.1016/j.bulsci.2019.102794</a>.
  ieee: K. N. Destagnol and E. Sofos, “Rational points and prime values of polynomials
    in moderately many variables,” <i>Bulletin des Sciences Mathematiques</i>, vol.
    156, no. 11. Elsevier, 2019.
  ista: Destagnol KN, Sofos E. 2019. Rational points and prime values of polynomials
    in moderately many variables. Bulletin des Sciences Mathematiques. 156(11), 102794.
  mla: Destagnol, Kevin N., and Efthymios Sofos. “Rational Points and Prime Values
    of Polynomials in Moderately Many Variables.” <i>Bulletin Des Sciences Mathematiques</i>,
    vol. 156, no. 11, 102794, Elsevier, 2019, doi:<a href="https://doi.org/10.1016/j.bulsci.2019.102794">10.1016/j.bulsci.2019.102794</a>.
  short: K.N. Destagnol, E. Sofos, Bulletin Des Sciences Mathematiques 156 (2019).
date_created: 2019-09-01T22:00:55Z
date_published: 2019-11-01T00:00:00Z
date_updated: 2023-08-29T07:18:02Z
day: '01'
department:
- _id: TiBr
doi: 10.1016/j.bulsci.2019.102794
external_id:
  arxiv:
  - '1801.03082'
  isi:
  - '000496342100002'
intvolume: '       156'
isi: 1
issue: '11'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1801.03082
month: '11'
oa: 1
oa_version: Preprint
publication: Bulletin des Sciences Mathematiques
publication_identifier:
  issn:
  - 0007-4497
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Rational points and prime values of polynomials in moderately many variables
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 156
year: '2019'
...