By V. Balaji, C. S. Seshadri (auth.), Akira Fujiki, Kazuya Kato, Yujiro Kawamata, Toshiyuki Katsura, Yoichi Miyaoka (eds.)

The overseas convention "Algebraic Geometry and Analytic Geometry, Tokyo 1990" used to be held at Tokyo Metropolitan college and the Tokyo education heart of Daihyaku Mutual existence assurance Co., from August thirteen via August 17, 1990, lower than the co-sponsorship of the Mathematical Society of Japan. It used to be one of many satellite tv for pc meetings of ICM90, Kyoto, and nearly three hundred individuals, together with greater than a hundred from in a foreign country, attended the convention. the educational application was once divided into elements, the morning classes and the afternoon periods. The morning periods have been held at Tokyo Metropolitan collage, and one-hour plenary lectures have been brought each day. The afternoon classes on the Tokyo education middle, meant for a extra really expert viewers, consisted of 4 separate subsessions: Arithemetic Geometry, Algebraic Geometry, Analytic Geometry I and Analytic Geometry II. This ebook comprises papers which grew out of the talks on the convention. The committee in control of the association and software consisted of A. Fujiki, ok. Kato, T. Katsura, Y. Kawamata, Y. Miyaoka, S. Mori, okay. Saito, N. Sasakura, T. Suwa and ok. Watanabe. we wish to take this chance to thank the numerous mathematicians and scholars who cooperated to make the convention attainable, specifically Professors T. Fukui, S. Ishii, Y. Kitaoka, M. Miyanishi, Y. Namikawa, T. Oda, F. Sakai and T. Shioda for his or her useful recommendation and suggestions in organizing this convention. monetary help was once in general supplied via own contributions from Professors M.

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W"x/y for then 75 is ample. The same result, for moduli of K3 surfaces, is due to Pjatetskij-Sapiro and Safarevich [12]. The final version of [16] will contain a discussion of ample sheaves on Ph in the general case, building up on the results explained here. This note does not really contain any substantially new ideas. 1) and of the ampleness of Av to recall and clarify some of methods from [3] and [14], III. In §1 we consider the relation between weak positivity and ampleness. §2 contains a discussion of the invariant e(r) introduced in [3] to measure the singularities of a divisor f on some manifold X.

T is defined purely in terms of projective structure on K* /k*. Namely fixing one point as 00 we define a reflection S;: with respect to any point. Then we define the summation by S[fS;;'x = x - 2a in case chark is not equal to two. Fixing points (1, -1) in pI we are able to define multiplicative operation in the field k,or more exactly in the set pI \ pt. For chark = 2 we need slightly more complicated products of Se;, ((3 is a root of unity in characteristic two field with more than two elements.

Also want to thank referee for useful remarks. Bogomolov "On the structure of abelian subgroups of the Galois groups"Izvestiya of the Academy of Science of the USSR(in russian) NI,I991 . 1011-1061. Ample sheaves on moduli schemes Helene Esnault Eckart Viehweg Universitiit - GH - Essen, Fachbereich 6, Mathematik Universitiitsstrafie 3, D-4300 Essen 1 , Germany In this note we take up methods from [3] and [14], III, to give some criteria for certain direct image sheaves to be ample. 1 Let f : X - t Y be a fiat projective Gorenstein morphism of complex reduced schemes whose fibres are irreducible normal varieties with at worst rational singularities.

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