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)
- W. P. Barth, "Polyhedral groups and pencils of K3-surfaces with maximal Picard number", Asian J. Math, 7(4), pp.519~538 (2003)[DOI]
- S. Boissière, "Counting lines on surfaces", Ann. Sc. Norm. Super. Pisa Cl. Sci, 6(1), pp.39~52 (2007)
- "Magma codes for “Some singular curves and surfaces arising from invariants of complex reflection groups", preprint" (2018)[URL]
- C. Bonnafé, "Some singular curves and surfaces arising from invariants of complex reflection groups", Exp. Math, 30(3), pp.429~440 (2021)[DOI]
- C. Bonnafé, "Complex reflection groups and K3 surfaces I, Épijournal Géom", Algébrique, 5, pp.26~ (2021)[DOI]
- C. Bonnafé, "K3 surfaces with maximal finite automorphism groups containing M20", Ann. Inst. Fourier(Grenoble), 71(2), pp.711~730 (2021)
- C. Bonnafé, "Complex reflection groups and K3 surfaces III The group G28 = W(F4), in preparation", ~
- W. Bosma, "The Magma algebra system. I. The user language", J. Symbolic Comput, 24(3-4), pp.235~265 (1997)[DOI]
- N. Bourbaki, "Groupes et algèbres de Lie, Chapitres 4, 5, 6" (1968), Hermann
- A. I. Degtyarev, "800 conics on a smooth quartic surface", J. Pure Appl. Algebra, 226(10), pp.5~ (2022)[DOI]
- 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]
- D. Festi, "Counting elliptic fibrations on K3 surfaces, preprint", ~ (2021)
- 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)
- G. Lusztig, "Some examples of square integrable representations of semisimple p-adic groups", Trans. Amer. Math. Soc, 277(2), pp.623~653 (1983)[DOI]
- I. Marin, "Automorphisms of complex reflection groups", Represent. Theory, 14, pp.747~788 (2010)[DOI]
- J. C. M. Michel, "The development version of the CHEVIE package of GAP3", J. Algebra, 435, pp.308~336 (2015)[DOI]
- S. Mukai, "Finite groups of automorphisms of K3 surfaces and the Mathieu group", Invent. Math, 94(1), pp.183~221 (1988)[DOI]
- B. Naskręcki, "Explicit equations of 800 conics on a Barth-Bauer quartic", ~
- N. O. Nygaard, "Tate’s conjecture for K3 surfaces of finite height", Ann. of Math, 122(3), pp.461~507 (1985)[DOI]
- A. Sarti, "Pencils of symmetric surfaces in P3", J. Algebra, 246(1), pp.429~452 (2001)[DOI]
- A. Sarti, "Transcendental lattices of some K3-surfaces", Math. Nachr, 281(7), pp.1031~1046 (2008)[DOI]
- M. Schütt, "Elliptic fibrations of some extremal K3 surfaces", Rocky Mountain J. Math, 37(2), pp.609~652 (2007)[DOI]
- M. Schütt, "Mordell-Weil lattices, Ergebnisse der Mathematik und ihrer Grenzgebiete" (2019), Springer
- G. C. Shephard, "Finite unitary reflection groups", Canad. J. Math, 6, pp.274~304 (1954)[DOI]
- I. Shimada, "On elliptic K3 surfaces", Michigan Math. J, 47(3), pp.423~446 (2000)[DOI]
- H. Sterk, "Finiteness results for algebraic K3 surfaces", Math. Z, 189(4), pp.507~513 (1985)[DOI]
- U. Thiel, "Champ : a Cherednik algebra Magma package", LMS J. Comput. Math, 18(1), pp.266~307 (2015)[DOI]
- R. M. van Luijk, "Quartic K3 surfaces without nontrivial automorphisms", Math. Res. Lett, 13(2-3), pp.423~439 (2006)[DOI]
- 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]
- G. Xiao, "Galois covers between K3 surfaces", Ann. Inst. Fourier(Grenoble), 46(1), pp.73~88 (1996)
관련 논문AI추천
Classification of order sixteen non-symplectic automorphisms on K3 surfacesAlessandra Sarti, Dima Al Tabbaa, Shingo Taki대한수학회 · 대한수학회지2016 · 제53권 제6호Some Siegel Threefolds with a Calabi-Yau Model IIEberhard Freitag, Riccardo Salvati Manni경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2013 · 제53권 제2호Extending hyperelliptic K3 surfaces, and Godeaux surfaces with $\pi_1=\mathbb{Z}/2$Stephen Coughlan대한수학회 · 대한수학회지2016 · 제53권 제4호AUTOMORPHISMS OF K3 SURFACES WITH PICARD NUMBER TWO이광우대한수학회 · 대한수학회보2023 · 제60권 제6호Which K3 surfaces with Picard number 19 cover an Enriques surface이광우대한수학회 · 대한수학회보2012 · 제49권 제1호Smooth, isolated curves in families of Calabi-Yau threefolds in homogeneous spacesAndreas Leopold Knutsen대한수학회 · 대한수학회지2013 · 제50권 제5호
이 간행물의 다른 논문 (8건)
Some algebras having relations like those for the 4-dimensional Sklyanin algebrasAlexandru Chirvasitu, S. Paul Smithpp. 745-777Computations and conservativeness of traces of one-dimensional diffusionsRafed Moussa, Ali BenAmorpp. 779-797Construction of a Mattila--Sj\"{o}lin type function over a finite field김진범, 정대웅pp. 799-822Cup product on relative bounded cohomology박희숙pp. 823-833Classification of solvable lie algebras whose non-trivial coadjoint orbits of simply connected lie groups are all of codimension 2Vu Anh Le, Tu Thi Cam Nguyen, Hoa Duong Quang, Hieu Van Happ. 835-858
