Families of Meromorphic Functions on Compact Riemann Surfaces

Namba, Makoto

doi:10.1007/bfb0085979

Cited by 57 publications

(43 citation statements)

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“…which ensures commutativity of the following: 22 There is a natural extension of the deformation theory of holomorphic maps developed by Namba [70], wherein the complex structures of both V and U are varied. This, however, would only become relevant if we studied YM 2 coupled to 2d (spacetime) gravity.…”

Section: What About Qcd4?mentioning

confidence: 99%

“…This is the analogue of the Kodaira-Spencer map which arises in the study of deformations of the complex structures of complex manifolds. In order to present this description of the tangent space to F , we need to introduce a few more notions: First we introduce the following complex of sheaves [70]:…”

Section: What About Qcd4?mentioning

confidence: 99%

“…One important property of F which is of obvious interest is its dimension. For this purpose the following two theorems due to Horikawa [68] and Namba [70] Theorem: [Namba] The following sequence is exact:…”

Section: −→ Smentioning

confidence: 99%

“…The deformation theory of holomorphic maps is a subject developed by Horikawa [68], Mijayima [69] and Namba [70]. Let U be a fixed compact complex manifold.…”

Section: Acknowledgementsmentioning

confidence: 99%

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Large N 2D Yang-Mills Theory and Topological String Theory

Cordes

Moore

Ramgoolam

1997

Communications in Mathematical Physics

103

211

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We describe a topological string theory which reproduces many aspects of the 1/N expansion of SU (N ) Yang-Mills theory in two spacetime dimensions in the zero coupling (A = 0) limit. The string theory is a modified version of topological gravity coupled to a topological sigma model with spacetime as target. The derivation of the string theory relies on a new interpretation of Gross and Taylor's "Ω −1 points." We describe how inclusion of the area, coupling of chiral sectors, and Wilson loop expectation values can be incorporated in the topological string approach.

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Section: What About Qcd4?mentioning

confidence: 99%

Section: What About Qcd4?mentioning

confidence: 99%

Section: −→ Smentioning

confidence: 99%

“…The deformation theory of holomorphic maps is a subject developed by Horikawa [68], Mijayima [69] and Namba [70]. Let U be a fixed compact complex manifold.…”

Section: Acknowledgementsmentioning

confidence: 99%

See 2 more Smart Citations

Large N 2D Yang-Mills Theory and Topological String Theory

Cordes

Moore

Ramgoolam

1997

Communications in Mathematical Physics

103

211

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“…is birationally equivalent to a smooth projective plane curve of degree d, hence of gonality d − 1 by a result of Namba [38] (a proof can also be found in [43,Prop. 3.13]).…”

Section: Gonalitymentioning

confidence: 88%

Linear Pencils Encoded in the Newton Polygon

Castryck

Cools

2016

Int Math Res Notices

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Abstract. Let C be an algebraic curve defined by a sufficiently generic bivariate Laurent polynomial with given Newton polygon ∆. It is classical that the geometric genus of C equals the number of lattice points in the interior of ∆. 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 to 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 n th Hirzebruch surface H n , then n is actually an invariant of C.

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Gonality of complete graphs with a small number of omitted edges

Panizzut

2016

Mathematische Nachrichten

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Let K d be the complete metric graph on d vertices. We compute the gonality of graphs obtained from K d by omitting edges forming a K h , or general configurations of at most d − 2 edges. We also investigate if these graphs can be lifted to curves with the same gonality. We lift the former graphs and the ones obtained by removing up to d − 2 edges not forming a K 3 using models of plane curves with certain singularities. We also study the gonality when removing d − 1 edges not forming a K 3 . We use harmonic morphism to lift these graphs to curves with the same gonality because in this case plane singular models can no longer be used due to a result of Coppens and Kato.

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Families of Meromorphic Functions on Compact Riemann Surfaces

Cited by 57 publications

References 0 publications

Large N 2D Yang-Mills Theory and Topological String Theory

Large N 2D Yang-Mills Theory and Topological String Theory

Linear Pencils Encoded in the Newton Polygon

Gonality of complete graphs with a small number of omitted edges

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