Fumio Sakai - Academia.edu (original) (raw)

Papers by Fumio Sakai

数理解析研究所講究録, Sep 1, 1992

Zariski [Z1], [Z2]. My personal motivation te this question is its application to the analysis of... more Zariski [Z1], [Z2]. My personal motivation te this question is its application to the analysis of singular plane curves. Cf. [S].

Lecture Notes in Mathematics, 1979

We introduce and study coordinate-wise powers of subvarieties of P n , i.e. varieties arising fro... more We introduce and study coordinate-wise powers of subvarieties of P n , i.e. varieties arising from raising all points in a given subvariety of P n to the r-th power, coordinate by coordinate. This corresponds to studying the image of a subvariety of P n under the quotient of P n by the action of the finite group Z n+1 r. We determine the degree of coordinate-wise powers and study their defining equations, in particular for hypersurfaces and linear spaces. Applying these results, we compute the degree of the variety of orthostochastic matrices and determine iterated dual and reciprocal varieties of power sum hypersurfaces. We also establish a link between coordinate-wise squares of linear spaces and the study of real symmetric matrices with a degenerate eigenspectrum.

Osaka Journal of Mathematics, 2000

A plane curve C C P = P(C) is said to be of type (d, v) if the degree of C is d and the maximal m... more A plane curve C C P = P(C) is said to be of type (d, v) if the degree of C is d and the maximal multiplicity of C is υ. In case C is rational and cuspidal, we have proved the inequality: d < 3v ([4]). A cusp means a unibranched (i.e., locally irreducible) singular point. Rational cuspidal curves of type (d, d — 2) are classified in [2] under the assumption that C has at least three cusps. The type (d, d — 3) case with at least three cusps is also discussed in [3]. In this note, we classify rational cuspidal curves of type (d, d — 2) having at most two cusps. For a cusp P e C, let m_p = (mo,/>, ... , wn+ι,/>) denote the multiplicity sequence ([2, 3, 4]), where mo,/> is the multiplicity m/> = m/>(C) of C at P. The notation (24) means the sequence (2, 2, 2, 2, 1, 1). We prove the following

In this paper, we study the geometry of the 2-Weierstrass points on the Kuribayashi quartic curve... more In this paper, we study the geometry of the 2-Weierstrass points on the Kuribayashi quartic curves: Ca : x 4 + y + z + a(xy + yz + xz) = 0 (a = 1,±2). The 2-Weierstrass points on Ca are divided into flexes and sextactic points. It is known that the symmetric group S4 acts on Ca (See [8]). Using the S4-action, we classify the 2-Weierstrass points on Ca.

Contemporary Mathematics, 1994

Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1989

Characterization of Ball Quotients 239 a.l or all a (resp. a. 1 for all a and bfor all i). This d... more Characterization of Ball Quotients 239 a.l or all a (resp. a. 1 for all a and bfor all i). This definition does not depend on the choice of a good resolution. A log-canonical singularity is LCS if it is not log-terminal, i.e. some coefficients in D+A is equal to 1. Nakamura [11] classified log-canonical singularities and showed that all log-canonical singularities are quotient singularities in a broad sense, namely, they are uniformized by bounded symmetric domains"

We classify the 3-Weierstrass points on genus two curves y 2 =x 6 +ax 4 +bx 2 +1, where a,b∈ℂ are... more We classify the 3-Weierstrass points on genus two curves y 2 =x 6 +ax 4 +bx 2 +1, where a,b∈ℂ are parameters. We describe the classification in terms of the invariants u=ab and v=a 3 +b 3 (see [T. Shaska and H. Völklein, in: Algebra, arithmetic and geometry with applications. Papers from Shreeram S. Ahhyankar’s 70th birthday conference, Purdue University, West Lafayette, IN, USA, July 19–26, 2000. Berlin: Springer 703–723 (2003; Zbl 1093.14036)].

In a previous paper, we classified and constructed all rational plane curves of type (d,d-2). In ... more In a previous paper, we classified and constructed all rational plane curves of type (d,d-2). In this paper, we generalize these results to irreducible plane curves of type (d,d-2) with positive genus.

Tokyo Journal of Mathematics, 2004

Manuscripta Mathematica, 1985

For a rank 2 vector bundle E on a non-singular projective curve of genus g, the theorem of Nagata... more For a rank 2 vector bundle E on a non-singular projective curve of genus g, the theorem of Nagata tells us that deg E-2 max deg F?g where the maximum is taken over all sub line bundles F of E. We generalize this result to vector bundles of arbitrary rank.

Journal of the Mathematical Society of Japan, 1988

A minimal ruled fibration will mean a ruled fibration whose fibres contain no exceptional curves ... more A minimal ruled fibration will mean a ruled fibration whose fibres contain no exceptional curves of the first kind. Given a ruled fibration on YYY , contract successively all exceptional curves of the first kind in fibres, then we obtain a minimal ruled fibration.

Duke Mathematical Journal, 1984

Archiv der Mathematik, 2013

In this note, we prove a necessary and sufficient condition for whether a d-cyclic covering of th... more In this note, we prove a necessary and sufficient condition for whether a d-cyclic covering of the complex projective line has gonality 2 (i.e., is elliptic or hyperelliptic), where d is a positive integer. The case of 3 branch points has been solved in our previous paper (see [3]).

American Journal of Mathematics, 1982

代数幾何学シンポジューム, Nov 15, 1982