Showing papers in "Tohoku Mathematical Journal in 1979"

On Fermat varieties

Abstract: (0.1) x? + x? + + x?+ί = 0 . Throughout this paper, we denote it by Xrm, or by X r m(p), when we need to specify the characteristic p of the base field k; we always assume that m ^ 0 (mod p). The purpose of this paper is to clarify the "inductive structure" of Fermat varieties of a common degree and of various dimensions, and apply it to the questions concerning the unirationality and algebraic cycles of a Fermat variety. The main results are stated as follows: THEOREM I. For any positive integers r and s, XZf is obtained from the product Xrm x X 8 m by 1) blowing up a subvariety isomorphic to X~ x X'*, 2) taking the quotient of the blown up variety with respect to an action of the cyclic group of order m, and 3) blowing down from the quotient two subvarieties isomorphic to P x X'ΰ and Xlr x P\

The first eigenvalue of the laplacian on spheres

Abstract: where Vol(S2, h) denotes the volume of S2 with respect to h. Equality in (*) or (**) holds if and only if h is a constant curvature metric. M. Berger [1] showed that (*) cannot be generalized for (Sm, h), m>_3. With respect to (* *), M. Berger [1] posed a problem: Let M be a compact smooth manifold; then does there exist a constant k(M) depending only on M such that the first eigenvalue 1(h) of the Laplacian satisfies

Remark on a characterization of bmo-martingales

Abstract: REFERENCES[ 1 ] C. DoLέANS-DADE AND P. A. MEYER, Iπegalites de normes avec poids, (preprint).[2] C. DθLέANS-DADE AND P. A. MEYER, Une caracterisation de BMO, Seminaire de Pro-babilites XI, Univ. de Strasbourg, Lecture Notes in Math., 581 (1977), Springer-Verlag, Berlin, 383-389.] 3 ] M. IZUMISAWA AND N. KAZAMAKI, Weighted norm inequalities for martingales, TδhokuMath. J., 29 (1977), 115-124.[4] N. KAZAMAKI, On transforming the class of BMO-martingales by a change of law,