List of Publications

Papers

  • Elliptic fibrations of maximal rank on a supersingular K3 surface, submitted to Shaf90 issue,Izvestia RAS, Ser. Math. (2012)(PDF).
  • (with Abhinav Kumar) Multiplicative excellent families of elliptic surfaces of type E7 or E8, arXiv 1204/1531
  • Multiplicative excellent family of type E6, Proc. Japan Acad. 86A, 21?26 (2012).
  • (with Matthias Schuett and Ronald van Luijk) Lines on Fermat surfaces, Jounal of Number Theory 130,1939-1963(2010)(PDF).
  • (with Matthias Schuett) Elliptic surfaces, in: Algebraic Geometry in East Asia---Seoul 2008, Advanced Studies in Pure Mathematics 60,51-160(2010)(PDF).
  • Grobner basis,Mordell-Weil lattices and deformation of singularities,I,Proc.Japan Acad.86A,21-26 (2010).
  • Grobner basis,Mordell-Weil lattices and deformation of singularities,II,Proc.Japan Acad.86A,27-32 (2010).
  • (with Noboru Aoki) Correction and supplement to the paper:"Generators of the Neron-Severi group of a Fermat surface",Comment.Math.Univ.St.Pauli 59,65-75(2010)
  • Some explicit integral polynomials with Galois group $W(E_8)$, Proc. Japan Acad. 85A, 118--121 (2009).
  • Elliptic fibrations of maximal rank on a supersingular K3 surface, (in preparation).
  • Grobner basis, Mordell-Weil lattices and deformation of singularities, Preprint RIMS-1661,March 2009,Kyoto Univ..(PDF)
  • The abc-theorem, Davenport 's inequality and elliptic surfaces, Proc.Japan Acad. 84A, 51-56 (2008).
  • K3 surfaces and sphere packings (PDF) , J.Math.Soc.Japan 60,1083-1105(2008).
  • (with M.Kuwata) Elliptic parameters and defining equations for elliptic fibrations on a Kummer surface, in: Algebraic Geometry in East Asia-Hanoi 2005, 177-215, Advanced Studies in Pure Mathematics 50 (2008).;(PDF)
  • (with Viet Nguyen-Khac) On the Castelnuovo-Weil lattices I, in: Algebraic Geomery in East Asia-Hanoi 2005, 333-344 , Adavanced Studies in Pure Mathematics 50(2008).
  • The Mordell-Weil lattice of y2=x3 + t5 - 1/t5 -11 , Comment.Math. Univ. St. Pauli 56, 45--70 (2007). (PDF)
  • (with Matthias Schuett) An interesting elliptic surface over an elliptic curve, Proc. Japan Acad. 83A, 40--45 (2007). (PDF)
  • Correspondence of elliptic curves and Mordell-Weil lattices of certain elliptic K3 surfaces, in: Algebraic Cycles and Motives, vol. 2, 319--339, Cambridge Univ. Press (2007).(PDF)
  • Classical Kummer surfaces and Mordell-Weil lattices, in:Algebraic Geometry, Contemporary Mathematics 422, AMS, 213-221 (2007). (PDF)
  • Kummer sandwich theorem of certain elliptic K3 surfaces, Proc. Japan Acad. 82A, 137-140 (2006).(PDF)
  • On K3 surfaces defined over Q---- Correction to the paper [1] in Vol.43(1994), Comment. Math. Univ. St. Pauli 54, 87--89 (2005). (PDF) (DVI)
  • Elliptic surfaces and Davenport-Stothers triples, Comment. Math. Univ. St. Pauli 54, 49--68 (2005).(PDF) (DVI)
  • The elliptic $K3$ surfaces with a maximal singular fibre, C. R. Acad. Sci. Paris, Ser. I 336, 461--466 (2003).
  • Some codes arising from elliptic modular surfaces, Comment. Math. Univ. St. Pauli 51, 67-78 (2002).(PDF) (DVI)
  • Integral points and Mordell-Weil lattices, in: A Panorama in Number Theory or The View from Baker's Garden, Cambridge Univ. Press, 185--193 (2002).
  • A note on K3 surfaces and sphere packings, Proc. Japan Acad. 76A, 68--72 (2000).
  • Some new observation on invariant theory of plane quartics, Kodaira volume,Asian J. Math. 4, 227-234 (2000).
  • (with Y.Umezu) On N'eron's construction of curves with high rank, I, Comment. Math. Univ. St. Pauli 48, 35-47 (1999). (PDF)
  • Cyclotomic analogue in the theory of algebraic equations of type E_6, E_7, E_8, in: Integral Quadratic Forms and Lattices, Contemporary Mathematics 249, AMS, 87-96 (1999).
  • The splitting field of Mordell-Weil lattices, in: Algebraic Geometry: Hirzebruch 70, Contemporary Mathematics 241, AMS, 297-303 (1999). [3 drawings included]
  • (with T. Terasoma) Existence of simple Jacobian varieties of genus $g$ with rank at least $4g+5$, Am. J. Math. 121, 65--72 (1999).
  • On Q-split B'ezout intersection, J. Pure and Applied Algebra 135, 295--301 (1999).
  • Mordell-Weil lattices for higher genus fibration over a curve, in: New Trends in Algebraic Geometry, Cambridge Univ. Press, 359-373 (1999).
  • Constructing curves with high rank via symmetry, Am. J. Math. 120, 551-566 (1998).
  • Curves of genus two over Q (t) with high rank, Comment. Math. Univ. St. Pauli~46, 15--21 (1997).
  • A uniform construction of the root lattices $E_6, E_7, E_8$ and their dual lattices, Proc. Japan Acad.71A, 140--143 (1995).
  • The algebraic equation of type $E_6$ and Chebotarev density, Algebra and Analysis (Proc. Chebotarev centennial conference at Kazan Univ. June 1994 , ed. by Arslanov, Parshin, Shafarevich), Walter de Gruyter & Co. , 109--114 (1996).(PDF) (DVI)
  • Weierstrass transformations and cubic surfaces, Comment. Math. Univ. St. Pauli44, 109--128 (1995).(PDF) (DVI)
  • On the rank of elliptic curves over {bf Q}(t) arising from K3 surfaces, Comment. Math. Univ. St. Pauli 43, 117--120 (1994).(PDF) (DVI)
  • Plane quartics and Mordell-Weil lattices of type E_7, Comment. Math. Univ. St. Pauli 42, 61--79 (1993). (PDF)
  • Generalization of a theorem of Manin-Shafarevich, Proc. Japan Acad. 69A, 10--12 (1993).
  • Existence of a rational elliptic surface with a given Mordell-Weil lattice, Proc. Japan Acad. 68A, 251--255 (1992) (PDF)
  • Mordell-Weil lattices for higher genus fibration, Proc. Japan Acad. 68A, 247--250 (1992).
  • (with H. Usui) Fundamental invariants of Weyl groups and excellent families of elliptic curves, Comment. Math. Univ. St. Pauli 41, 169--217 (1992). (PDF)
  • Some remarks on elliptic curves over function fields, Proc. Journ'ees Arithm'etiques 91, Gen`eve, Ast'erisque 209, 99--114 (1992). (PDF)
  • Mordell-Weil lattices: Theory and applications--- A point of contact of algebra, geometry,... and computer (in Japanese), Sugaku 43, 97--114 (1991); Translation in: AMS Sugaku Expositions 7, 19--41 (1994).
  • (with K.Oguiso) The Mordell--Weil lattice of a rational elliptic surface, Comment. Math. Univ. St. Pauli~40, 83--99 (1991).(PDF)
  • An infinite family of elliptic curves over Q with large rank via N'eron's method, Invent. Math. 106, 109--119 (1991).
  • Mordell-Weil lattices and sphere packings, Am. J. Math. 113, 931--948 (1991).
  • Theory of Mordell-Weil lattices, in: Proc. ICM Kyoto--1990, vol. I, 473--489 (1991).
  • Construction of elliptic curves with high rank via the invariants of the Weyl groups, J. Math. Soc. Japan 43, 673--719 (1991).
  • Mordell-Weil lattices of type $E_8$ and deformation of singularities, in: Lecture Notes in Math. 1468, 177--202 (1991).
  • Construction of elliptic curves over Q (t) with high rank: a preview, Proc. Japan Acad. 66A, 57--60 (1990).
  • On the Mordell-Weil lattices, Comment. Math. Univ. St. Pauli 39, 211-- 240 (1990).(PDF)
  • Mordell-Weil lattices and Galois representation, I, II, III, Proc. Japan Acad. 65A, 267--271, 296--299, 300--303 (1989).

  • The Galois representation of type $E_8$ arising from certain Mordell-Weil groups, Proc. Japan Acad. 65A, 195--197 (1989).
  • Frey's elliptic curve as an elliptic surface over the Fermat curve, Comment. Math. Univ. St. Pauli 38, 223--232 (1989).
  • Arithmetic and geometry of Fermat curves, in: Proc. Alg. Geom. Sem. Singapore 1987, 95--102, World Scientific (1988).
  • Supersingular K3 surfaces with big Artin invariants, J. reine angew. Math.~381, 205--210 (1987).
  • Some observations on Jacobi sums, Adv. Studies in Pure Math. 12, 119--135 (1987).
  • Algebraic cycles on hypersurfaces in P^n, Adv.\ Studies in Pure Math. 10, 717--732 (1985).
  • A note on a theorem of Griffiths on the Abel--Jacobi map, Invent. Math. 82, 461--465 (1985).
  • An explicit algorithm for computing the Picard number of certain algebraic surfaces, Am. J. Math. 108, 415--432 (1986).
  • Algebraic cycles on a certain hypersurface, Lecture Notes in Math. 1016, 271--294 (1983).
  • (with N. Aoki) Generators of the N'eron--Severi group of a Fermat surface, in: Arithmetic and Geometry (dedicated to Shafarevich) vol.I, 1--12, Birkh"{a}user (1983).
  • What is known about the Hodge conjecture ?, Adv. Studies in Pure Math. 1, 55--68 (1983).
  • Geometry of Fermat varieties, in: Number Theory related to Fermat's Last Theorem, 45--56, Birkh"{a}user, 1982.
  • On the Picard number of a Fermat surface, J. Fac. Sci. Univ. Tokyo, Sec. IA28, 725--734 (1982).
  • Algebraic cycles on abelian varieties of Fermat type, Math. Ann.258, 65--80 (1981).
  • On the Picard number of a complex projective variety, Ann. Sci. E.N.S 14, 303--321 (1981).
  • The Hodge conjecture for Fermat varieties, Math. Ann. 245, 175--184 (1979).
  • (with T. Katsura) On Fermat varieties, Tohoku Math. J. 31, 97--115 (1979).
  •  Supersingular K3 surfaces, Lecture Notes in Math. 732, 564--591 (1979).
  • The period map of abelian surfaces, J. Fac. Sci. Univ. Tokyo, Sec. IA25, 47--59 (1978).
  • Some results on unirationality of algebraic surfaces, Math. Ann.230, 153--168 (1977).
  • On unirationality of supersingular surfaces, Math. Ann.225, 155--159 (1977).
  • Some remarks on abelian varieties, J. Fac. Sci. Univ. Tokyo, Sec.IA24, 11--21 (1977).
  • (with H. Inose), On singular K3 surfaces, in: Complex Analysis and Algebraic Geometry (dedicated to Kodaira), 119--136, Iwanami Shoten and Cambridge Univ. Press (1977).
  • An example of unirational surfaces in characteristic $p$, Math. Ann. 211, 233--236 (1974).
  • Kummer surfaces in characteristic~2, Proc. Japan Acad. 50, 718--722 (1974).
  • (with N. Mitani) Singular abelian surfaces and binary quadratic forms, Lecture Notes in Math. 412, 259--287 (1974).
  • Algebraic cycles on certain K3 surfaces in characteristic $p$, in: Proc. Int. Conf. on Manifolds--Tokyo 1973, 357--364, Univ. Tokyo Press (1975).
  • On rational points of the generic elliptic curve with level $N$ structure over the field of modular functions of level $N$, J. Math. Soc. Japan~25, 144--157 (1973).
  • On elliptic modular surfaces, J. Math. Soc. Japan 24, 20--59 (1972).
  • Elliptic modular surfaces, I, II, Proc. Japan Acad. 45, 786--790, 833-837 (1969).
  • On the graded ring of invariants of binary octavics, Am. J. Math.~89, 1022--1046 (1967).
  • On algebraic varieties uniformizable by bounded domains,Proc.Japan Acad. 39,617-619(1963).

Books

  • (coeditor with W. L. Baily, Jr.) Complex Analysis and Algebraic Geometry---A Collection of Papers Dedicated to K. Kodaira, Iwanami Shoten Publishers and Cambridge Univ.\ Press, 1977.
  • (coeditor with M. Raynaud) Algebraic Geometry--- Proc. Japan-France Conf. Tokyo/Kyoto 1982, Lecture Notes in Math.~1016, Springer Verlag, 1983.
  • A Collection: Mordell-Weil Lattices, MPI/91-Collection, Max-Planck-Institut f"ur Mathematik, Bonn, 1991.
  • Lectures on Mordell-Weil Lattices (in Japanese), Lectures in Math. Sciences, Univ. Tokyo, 1993.
  • Further Collection: Mordell-Weil Lattices, MPI97-a, Max-Planck-Institut f"ur Mathematik, Bonn, 1997.
  • The abc-theorem, elliptic surfaces and Mordell-Weil Lattices (in Japanese), Lecture Notes in Mathematical Sciences 4, Univ.\ Tokyo,  2008.

(updated: 7/7/2008)