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Ryo Kawaguchi

Other affiliations: Osaka University
Bio: Ryo Kawaguchi is an academic researcher from Nara Medical University. The author has contributed to research in topics: Physics & Line bundle. The author has an hindex of 3, co-authored 9 publications receiving 24 citations. Previous affiliations of Ryo Kawaguchi include Osaka University.

Papers
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Journal ArticleDOI
TL;DR: In this paper, it was shown that the Clifford index for curves on a compact smooth toric surface can be computed by pencils on the ambient surface, which can be read off from the lattice polygon associated to the curve.

8 citations

Journal ArticleDOI
TL;DR: In this paper, the gonality conjecture for curves on toric surfaces was proved for the first time, and it was extended to curves on Hirzebruch surfaces by Aprodu.
Abstract: The gonality is one of important invariants in the study of li near systems on curves. The gonality conjecture which was posed by Green and Lazarsfeld predicts that we can read off the gonality of a curve from any one line bundle of sufficiently large degree on the curve. This conjecture had been proved for curves on Hirzebruch surfaces by Aprodu. In this artlcle, we will extend this resu lt for curves on certain toric surfaces.

6 citations

29 May 2023
TL;DR: In this article , the authors studied a single-field inflation model in which the inflaton potential has an upward step between two slow-roll regimes by taking into account the finite width of the step.
Abstract: We study a single-field inflation model in which the inflaton potential has an upward step between two slow-roll regimes by taking into account the finite width of the step. We calculate the probability distribution function (PDF) of the curvature perturbation $P[{\cal{R}}]$ using the $\delta N$ formalism. The PDF has an exponential-tail only for positive ${\cal{R}}$ whose slope depends on the step width. We find that the tail may have a significant impact on the estimation of the primordial black hole abundance. We also show that the PDF $P[{\cal{R}}]$ becomes highly asymmetric on a particular scale exiting the horizon before the step, at which the curvature power spectrum has a dip. This asymmetric PDF may leave an interesting signature in the large scale structure such as voids.

5 citations

Journal ArticleDOI
TL;DR: For a convex lattice polytope having at least one interior lattice point, a lower bound for its volume is derived from Hibi's lower bound theorem for the $$h^{*}$$ -vector.
Abstract: For a convex lattice polytope having at least one interior lattice point, a lower bound for its volume is derived from Hibi’s lower bound theorem for the $$h^{*}$$ -vector. On the other hand, it is known that the sectional genus of a polarized variety has an upper bound, which is an extension of the Castelnuovo bound for the genus of a projective curve. In this paper, we prove the equivalence of these two bounds. Namely, a polarized toric variety has maximal sectional genus if and only if its associated polytope has minimal volume. This is a generalization of the known fact that polytopes corresponding to the anticanonical bundles of Gorenstein toric Fano varieties are reflexive polytopes (whose typical examples are minimal volume polytopes with only one interior lattice point).

3 citations


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Book
01 Jan 1984

45 citations

Journal ArticleDOI
TL;DR: In this paper, the authors give a combinatorial upper bound for the gonality of a curve defined by a bivariate Laurent polynomial with given Newton polygon, and provide proofs in a considerable number of special cases.
Abstract: We give a combinatorial upper bound for the gonality of a curve that is defined by a bivariate Laurent polynomial with given Newton polygon. We conjecture that this bound is generically attained, and provide proofs in a considerable number of special cases. One proof technique uses recent work of M. Baker on linear systems on graphs, by means of which we reduce our conjecture to a purely combinatorial statement.

33 citations

Journal ArticleDOI
TL;DR: In this article it was shown that every base-point free pencil whose degree equals or slightly exceeds the gonality is combinatorial, in the sense that it corresponds to projecting C along a lattice direction.
Abstract: Let C be an algebraic curve defined by a sufficiently generic bivariate Laurent polynomial with given Newton polygon Delta. It is classical that the geometric genus of C equals the number of lattice points in the interior of Delta. In this paper we give similar combinatorial interpretations for the gonality, the Clifford index, and the Clifford dimension, by removing a technical assumption from a recent result of Kawaguchi. More generally, the method shows that apart from certain well-understood exceptions, every base-point free pencil whose degree equals or slightly exceeds the gonality is combinatorial, in the sense that it corresponds to projecting C along a lattice direction. Along the way we prove various features of combinatorial pencils. For instance, we give an interpretation for the scrollar invariants associated with a combinatorial pencil, and show how one can tell whether the pencil is complete or not. Among the applications, we find that every smooth projective curve admits at most one Weierstrass semi-group of embedding dimension 2, and that if a non-hyperelliptic smooth projective curve C of genus g >= 2 can be embedded in the nth Hirzebruch surface H-n, then n is actually an invariant of C. This article comes along with three Magma files: basic_commands.m, gonal.m, neargonal.m

21 citations

01 Jan 2016
TL;DR: In this paper, the Fano 3-folds and their higher dimension-al analogues are classified over an arbitrary field k C C by applying the theory of vector bundles (in the case B2 = 1) and theory of extremal rays.
Abstract: The Fano 3-folds and their higher dimension- al analogues are classified over an arbitrary field k C C by applying the theory-of vector bundles (in the case B2 = 1) and the theory of extremal rays (in the case B2 - 2). An n-dimen- sional smooth projective variety X over k is a Fano manifold if its first Chern class cl(X) E H2(X, Z) is positive in the sense of Kodaira (Kodaira, K. (1954) Ann. Math. 60, 28-48) (or am- ple). If n = 3 and cl(X) generates H2(X, Z), then either (i) X is a complete intersection in a Grassmann variety G with respect to a homogeneous vector bundle E on G: the rank of E is equal to codimnX and X is isomorphic to the zero locus of a global section of E, (ii) X is a linear section of a 10-dimensional spinor variety X 0 C P15, or (iii) X is isomorphic to a double cover of Pk, a 3-dimensional quadric Qk, or a quintic del Pezzo 3-fold V5 C Pk. If n = 4 and cl(X) is divisible by 2, then X ) C is isomorphic to (a) a complete intersection in a homogeneous space or its double cover, (b) a product of P' and a Fano 3- fold, (c) the blow-up of Q4 C P5 along a line or along a conic, or (d) a Pl-bundle compactifying a line bundle on P3 or on Q3 cp4.

19 citations

Posted Content
TL;DR: In this article, the authors give a combinatorial upper bound for the gonality of a curve defined by a bivariate Laurent polynomial with given Newton polygon, and provide proofs in a considerable number of special cases.
Abstract: We give a combinatorial upper bound for the gonality of a curve that is defined by a bivariate Laurent polynomial with given Newton polygon. We conjecture that this bound is generically attained, and provide proofs in a considerable number of special cases. One proof technique uses recent work of M. Baker on linear systems on graphs, by means of which we reduce our conjecture to a purely combinatorial statement.

18 citations