1,721,031 research outputs found
A Numerical criterion for admissibility of semi-simple elements
Get PDFUsui, Sampei. A numerical criterion for admissibility of semi-simple elements. Tohoku Math. J. (2) 45 (1993), no. 4, 471--484.In this article, we shall generalize a theorem of Cattani and Kaplan on horizontal representations of SL(2). Their theorem plays an important role in the construction of their partial compactifications of the classifying spaces D modulo an arithmetic subgroup of Hodge structures of weight 2
Complex structures on partial compactifications of arithmetic quotients of classifying spaces of Hodge structures
Get PDFUsui, Sampei. Complex structures on partial compactifications of arithmetic quotients of classifying spaces of Hodge structures. Tohoku Math. J. (2) 47 (1995), no. 3, 405--429.We construct partial compactifications of arithmetic quotients of the classifying spaces of polarized Hodge structures of general weight by adding the restrictions of the 'tamest' nilpotent orbits to the invariant cycles, and introduce complex structures on them. We prove holomorphic extendability of period maps from a punctured disc whose monodromy logarithm satisfies a certain property. We also examine some geometric examples which can be settled within the present framework
Recovery of vanishing cycles by log geometry
Get PDFUsui, Sampei. Recovery of vanishing cycles by log geometry. Tohoku Math. J. (2) 53 (2001), no. 1, 1-36.We first construct compatible actions of the product of the unit interval and the unit circle as a monoid on a semi-stable degeneration of pairs and on the associated log topological spaces. Then we show that the log topological family is locally trivial in piecewise smooth category over the base, i.e., the associated log topological family recovers the vanishing cycles of the original semi-stable degeneration in the most naive sense. Using this result together with the log Riemann-Hilbert correspondence, we introduce two types of integral structure of the variation of mixed Hodge structure associated to a semi-stable degeneration of pairs
Borel-Serre spaces and spaces of SL(2)-orbits
Get PDFKato, Kazuya; Usui, Sampei. Borel-Serre Spaces and Spaces of SL(2)-Orbits. Algebraic Geometry 2000, Azumino, 321--382, Mathematical Society of Japan, Tokyo, Japan, 2002. doi:10.2969/aspm/03610321. https://projecteuclid.org/euclid.aspm/1548550684Advanced studies in pure mathematics, 3
Classifying spaces of degenerating mixed Hodge structures, I: Borel-Serre spaces
Get PDFKato, Kazuya; Nakayama, Chikara; Usui, Sampei. Classifying spaces of degenerating mixed Hodge structures, I: Borel–Serre spaces. Algebraic Analysis and Around: In honor of Professor Masaki Kashiwara's 60th birthday, 187--222, Mathematical Society of Japan, Tokyo, Japan, 2009. doi:10.2969/aspm/05410187. https://projecteuclid.org/euclid.aspm/1543447760Advanced studies in pure mathematics, 54Let D be the classifying space of mixed Hodge structures with polarized graded quotients. We construct a real analytic manifold with corners DBS which contains D as a dense open subset. This is the mixed Hodge theoretic version of the Borel-Serre space in the case of pure weight constructed by Borel-Ji and Kato-Usui
SUMMARY OF STUDIES OF CLOSED/OPEN MIRROR SYMMETRY FOR QUINTIC THREEFOLDS THROUGH LOG MIXED HODGE THEORY (Aspects of Mirror Symmetry)
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Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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