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Linear automorphisms of smooth hypersurfaces giving Galois points

Taro Hayashi
대한수학회 (The Korean Mathematical Society)|2021.05|대한수학회보 (Bulletin of the KMS)|제58권 제3호|pp. 617-635|DOI 10.4134/BKMS.b200428

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참고문헌

키워드

automorphismSmooth hypersurfaceGalois pointGalois extension
주제분류수학

초록

Let $X$ be a smooth hypersurface $X$ of degree $d\geq4$ in a projective space $\mathbb P^{n+1}$. We consider a projection of $X$ from $p\in\mathbb P^{n+1}$ to a plane $H\cong\mathbb P^n$. This projection induces an extension of function fields $\mathbb C(X)/\mathbb C(\mathbb P^n)$. The point $p$ is called a Galois point if the extension is Galois. In this paper, we will give necessary and sufficient conditions for $X$ to have Galois points by using linear automorphisms.

Abstract

Let $X$ be a smooth hypersurface $X$ of degree $d\geq4$ in a projective space $\mathbb P^{n+1}$. We consider a projection of $X$ from $p\in\mathbb P^{n+1}$ to a plane $H\cong\mathbb P^n$. This projection induces an extension of function fields $\mathbb C(X)/\mathbb C(\mathbb P^n)$. The point $p$ is called a Galois point if the extension is Galois. In this paper, we will give necessary and sufficient conditions for $X$ to have Galois points by using linear automorphisms.

참고문헌 (24)

  1. Eslam Badr, "Non-singular plane curves with an element of “large” order in its automorphism group", International Journal of Algebra and Computation, 26(02), pp.399~433 (2016), World Scientific Pub Co Pte Lt[DOI]
  2. Eslam Badr, "Automorphism Groups of Nonsingular Plane Curves of Degree 5", Communications in Algebra, 44(10), pp.4327~4340 (2016), Informa UK Limited[DOI]
  3. F. Bastianelli, "The gonality theorem of Noether for hypersurfaces", Journal of Algebraic Geometry, 23(2), pp.313~339 (2014), American Mathematical Society (AMS)[DOI]
  4. Satoru Fukasawa, "Quasi-Galois points, I: Automorphism groups of plane curves", Tohoku Mathematical Journal, 71(4), pp.487~494 (2019), Mathematical Institute, Tohoku University[DOI]
  5. Satoru Fukasawa, "Galois points for a normal hypersurface", Transactions of the American Mathematical Society, 366(3), pp.1639~1658 (2014), American Mathematical Society (AMS)[DOI]
  6. Víctor González-Aguilera, "Automorphisms of prime order of smooth cubic n-folds", Archiv der Mathematik, 97(1), pp.25~37 (2011), Springer Science and Business Media LLC[DOI]
  7. Víctor González-Aguilera, "On the order of an automorphism of a smooth hypersurface", Israel Journal of Mathematics, 197(1), pp.29~49 (2013), Springer Science and Business Media LLC[DOI]
  8. Takeshi Harui, "Automorphism groups of smooth plane curves", Kodai Mathematical Journal, 42(2), pp.308~331 (2019), Tokyo Institute of Technology, Department of Mathematics[DOI]
  9. Takeshi Harui, "Automorphism group of plane curve computed by Galois points, II", Proceedings of the Japan Academy, Series A, Mathematical Sciences, 94(6), pp.59~63 (2018), Project Euclid[DOI]
  10. T. Hayashi, "Smooth plane curves with freely acting finite groups", Vietnam J. Math (2020)[DOI]
  11. M. Kanazawa, "The group generated by automorphisms belonging to Galois points of the quartic surface", Nihonkai Math. J, 12(1), pp.89~99 (2001)
  12. Jiryo Komeda, "RELATING GALOIS POINTS TO WEAK GALOIS WEIERSTRASS POINTS THROUGH DOUBLE COVERINGS OF CURVES", 대한수학회지, 54(1), pp.69~86 (2017), 대한수학회
  13. J. Komeda, "Galois Weierstrass points whose Weierstrass semigroups are generated by two elements", arXiv:1703.09416, ~
  14. H. Matsumura, "On the automorphisms of hypersurfaces", J. Math. Kyoto Univ, 3, pp.347~361 (1963)[DOI]
  15. Kei Miura, "Automorphism group of plane curve computed by Galois points", Beiträge zur Algebra und Geometrie, 2015, pp.56(2), 695~702[DOI]
  16. Kei Miura, "Field Theory for Function Fields of Plane Quartic Curves", Journal of Algebra, 226(1), pp.283~294 (2000), Elsevier BV[DOI]
  17. M. Noether, "Grundlegung der Theorie der algebraischen Raumcurven", J. Reine Angew. Math, 1882(93), pp.271~318 (1882), Walter de Gruyter GmbH[DOI]
  18. Keiji Oguiso, "Automorphism groups of smooth quintic threefolds", Asian Journal of Mathematics, 23(2), pp.201~256 (2019), International Press of Boston[DOI]
  19. T. Takahashi, "Galois points on normal quartic surfaces", Osaka J. Math, 39(3), pp.647~663 (2002)[DOI]
  20. H. Yoshihara, "Degree of Irrationality of an Algebraic Surface", Journal of Algebra, 167(3), pp.634~640 (1994), Elsevier BV[DOI]
  21. Hisao Yoshihara, "Function Field Theory of Plane Curves by Dual Curves", Journal of Algebra, 239(1), pp.340~355 (2001), Elsevier BV[DOI]
  22. H. Yoshihara, "Galois points on quartic surfaces", J. Math. Soc. Japan, 53(3), pp.731~743 (2001)[DOI]
  23. Hisao Yoshihara, "Galois points for smooth hypersurfaces", Journal of Algebra, 264(2), pp.520~534 (2003), Elsevier BV[DOI]
  24. Z. Zheng, "On abelian automorphism groups of hypersurfaces", arXiv : 2004. 09008, ~ (2020)

관련 논문AI추천

RELATING GALOIS POINTS TO WEAK GALOIS WEIERSTRASS POINTS THROUGH DOUBLE COVERINGS OF CURVESJiryo Komeda, Takeshi Takahashi대한수학회 · 대한수학회지2017 · 제54권 제1호Number of weak Galois-Weierstrass points with Weierstrass semigroups generated by two elementsJiryo Komeda, Takeshi Takahashi대한수학회 · 대한수학회지2019 · 제56권 제6호On extensions of double coverings of plane curves and Weierstrass semigroupsJiryo Komeda, Kenta Watanabe대한수학회 · 대한수학회보2025 · 제62권 제2호Conics on a general hypersurface in complex projective spaces신동수대한수학회 · 대한수학회보2013 · 제50권 제6호Some irrational quartic threefolds원준영, 홍규식대한수학회 · 대한수학회보2022 · 제59권 제2호Minimal del Pezzo surfaces of degree 2 over finite fieldsAndrey Trepalin대한수학회 · 대한수학회보2017 · 제54권 제5호

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