본문 바로가기
KERD
논문KCI 등재

Complex reflection groups and K3 surfaces II. The groups ${\boldsymbol{G_{29}}}$, ${\boldsymbol{G_{30}}}$ and ${\boldsymbol{G_{31}}}$

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

주제분류수학

초록

We study some K3 surfaces obtained as minimal resolutions of quotients of subgroups of special reflection groups. Some of these were already studied in a previous paper by W.~Barth and the second author. We give here an easy proof that these are K3 surfaces, give equations in weighted projective space and describe their geometry.

Abstract

We study some K3 surfaces obtained as minimal resolutions of quotients of subgroups of special reflection groups. Some of these were already studied in a previous paper by W.~Barth and the second author. We give here an easy proof that these are K3 surfaces, give equations in weighted projective space and describe their geometry.

참고문헌 (30)

  1. W. P. Barth, "Polyhedral groups and pencils of K3-surfaces with maximal Picard number", Asian J. Math, 7(4), pp.519~538 (2003)[DOI]
  2. S. Boissière, "Counting lines on surfaces", Ann. Sc. Norm. Super. Pisa Cl. Sci, 6(1), pp.39~52 (2007)
  3. "Magma codes for “Some singular curves and surfaces arising from invariants of complex reflection groups", preprint" (2018)[URL]
  4. C. Bonnafé, "Some singular curves and surfaces arising from invariants of complex reflection groups", Exp. Math, 30(3), pp.429~440 (2021)[DOI]
  5. C. Bonnafé, "Complex reflection groups and K3 surfaces I, Épijournal Géom", Algébrique, 5, pp.26~ (2021)[DOI]
  6. C. Bonnafé, "K3 surfaces with maximal finite automorphism groups containing M20", Ann. Inst. Fourier(Grenoble), 71(2), pp.711~730 (2021)
  7. C. Bonnafé, "Complex reflection groups and K3 surfaces III The group G28 = W(F4), in preparation", ~
  8. W. Bosma, "The Magma algebra system. I. The user language", J. Symbolic Comput, 24(3-4), pp.235~265 (1997)[DOI]
  9. N. Bourbaki, "Groupes et algèbres de Lie, Chapitres 4, 5, 6" (1968), Hermann
  10. A. I. Degtyarev, "800 conics on a smooth quartic surface", J. Pure Appl. Algebra, 226(10), pp.5~ (2022)[DOI]
  11. A.-S. Elsenhans, "The Picard group of a K3 surface and its reduction modulo p", Algebra Number Theory, 5(8), pp.1027~1040 (2011)[DOI]
  12. D. Festi, "Counting elliptic fibrations on K3 surfaces, preprint", ~ (2021)
  13. H. Inose, "On certain Kummer surfaces which can be realized as non-singular quartic surfaces in P3", J. Fac. Sci. Univ. Tokyo Sect. IA Math, 23(3), pp.545~560 (1976)
  14. G. Lusztig, "Some examples of square integrable representations of semisimple p-adic groups", Trans. Amer. Math. Soc, 277(2), pp.623~653 (1983)[DOI]
  15. I. Marin, "Automorphisms of complex reflection groups", Represent. Theory, 14, pp.747~788 (2010)[DOI]
  16. J. C. M. Michel, "The development version of the CHEVIE package of GAP3", J. Algebra, 435, pp.308~336 (2015)[DOI]
  17. S. Mukai, "Finite groups of automorphisms of K3 surfaces and the Mathieu group", Invent. Math, 94(1), pp.183~221 (1988)[DOI]
  18. B. Naskręcki, "Explicit equations of 800 conics on a Barth-Bauer quartic", ~
  19. N. O. Nygaard, "Tate’s conjecture for K3 surfaces of finite height", Ann. of Math, 122(3), pp.461~507 (1985)[DOI]
  20. A. Sarti, "Pencils of symmetric surfaces in P3", J. Algebra, 246(1), pp.429~452 (2001)[DOI]
  21. A. Sarti, "Transcendental lattices of some K3-surfaces", Math. Nachr, 281(7), pp.1031~1046 (2008)[DOI]
  22. M. Schütt, "Elliptic fibrations of some extremal K3 surfaces", Rocky Mountain J. Math, 37(2), pp.609~652 (2007)[DOI]
  23. M. Schütt, "Mordell-Weil lattices, Ergebnisse der Mathematik und ihrer Grenzgebiete" (2019), Springer
  24. G. C. Shephard, "Finite unitary reflection groups", Canad. J. Math, 6, pp.274~304 (1954)[DOI]
  25. I. Shimada, "On elliptic K3 surfaces", Michigan Math. J, 47(3), pp.423~446 (2000)[DOI]
  26. H. Sterk, "Finiteness results for algebraic K3 surfaces", Math. Z, 189(4), pp.507~513 (1985)[DOI]
  27. U. Thiel, "Champ : a Cherednik algebra Magma package", LMS J. Comput. Math, 18(1), pp.266~307 (2015)[DOI]
  28. R. M. van Luijk, "Quartic K3 surfaces without nontrivial automorphisms", Math. Res. Lett, 13(2-3), pp.423~439 (2006)[DOI]
  29. R. M. van Luijk, "K3 surfaces with Picard number one and infinitely many rational points", Algebra Number Theory, 1(1), pp.1~15 (2007)[DOI]
  30. G. Xiao, "Galois covers between K3 surfaces", Ann. Inst. Fourier(Grenoble), 46(1), pp.73~88 (1996)

관련 논문AI추천

이 간행물의 다른 논문 (8건)