Minitwistor spaces, Severi varieties, and Einstein–Weyl structure

Honda, Nobuhiro; Nakata, Fuminori

doi:10.1007/s10455-010-9235-z

Cited by 7 publications

(4 citation statements)

References 17 publications

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“…More recently, the author and Fuminori Nakata [12] have defined the minitwistor spaces to be complex surfaces which have a nodal rational curve having appropriate selfintersection numbers and showed that the space of such curves always becomes EinsteinWeyl 3-manifolds. This naturally generalizes Hitchin's minitwistor spaces and their associated Einstein-Weyl 3-manifolds given in [7].…”

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confidence: 99%

A new series of compact minitwistor spaces and Moishezon twistor spaces over them

Honda¹

2010

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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In recent papers [10], [11], we gave explicit description of some new Moishezon twistor spaces. In this paper, developing the method in the papers much further, we explicitly give projective models of a number of new Moishezon twistor spaces, as conic bundles over some rational surfaces (called minitwistor spaces). These include the twistor spaces studied in the papers as very special cases.Our source of the result is a series of self-dual metrics with torus action constructed by D. Joyce [15]. Actually, for arbitrary Joyce metrics and Uð1Þ-subgroups of the torus which fixes a torus-invariant 2-sphere, we first determine the associated minitwistor spaces in explicit forms. Next by analyzing the meromorphic maps from the twistor spaces to the minitwistor spaces, we realize projective models of the twistor spaces of all Joyce metrics, as conic bundles over the minitwistor spaces. Then we prove that for any one of these minitwistor spaces, there exist Moishezon twistor spaces with only C Ã -action whose quotient space is the given minitwistor space. This result generates numerous Moishezon twistor spaces which cannot be found in the literature (including the author's papers), in quite explicit form.

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confidence: 99%

A new series of compact minitwistor spaces and Moishezon twistor spaces over them

Honda¹

2010

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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“…In the article [6], we showed that the same result about the presence of Einstein-Weyl structure still holds even when the rational curves on a complex surface have ordinary nodes, as long as the complete family of such nodal rational curves on the surface is 3-dimensional. These nodal rational curves are still called minitwistor lines, and the number of nodes is called the genus of a minitwistor space.…”

Section: Introductionmentioning

confidence: 74%

On the cuspidal locus in the dual varieties of Segre quartic surface

Honda,

Minagawa

2021

Preprint

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Motivated by a kind of Penrose correspondence, we investigate the space of hyperplane sections of Segre quartic surfaces which have an ordinary cusp. We show that the space of such hyperplane sections is empty for two kinds of Segre surfaces, and it is a connected surface for all other kinds of Segre surfaces. We also show that when it is non-empty, the closure of the space is either birational to the surface itself or birational to a double covering of the surface, whose branch divisor consists of some specific lines on the surface.

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“…For some recent research on the Weyl geometry from the mathematical point of view, see e.g. [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

A modified variational principle for gravity in the modified Weyl geometry

Yuan¹,

Huang²

2013

Class. Quantum Grav.

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The usual interpretation of Weyl geometry is modified in two senses. First, both the additive Weyl connection and its variation are treated as (1, 2) tensors under the action of Weyl covariant derivative. Second, a modified covariant derivative operator is introduced which still preserves the tensor structure of the theory. With its help, the Riemann tensor in Weyl geometry can be written in a more compact form. We justify this modification in detail from several aspects and obtain some insights along the way. By introducing some new transformation rules for the variation of tensors under the action of Weyl covariant derivative, we find a Weyl version of Palatini identity for Riemann tensor. To derive the energy-momentum tensor and equations of motion for gravity in Weyl geometry, one naturally applies this identity at first, and then converts the variation of additive Weyl connection to those of metric tensor and Weyl gauge field. We also discuss possible connections to the current literature on Weyl-invariant extension of massive gravity and the variational principles in f(R) gravity.

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Minitwistor spaces, Severi varieties, and Einstein–Weyl structure

Cited by 7 publications

References 17 publications

A new series of compact minitwistor spaces and Moishezon twistor spaces over them

A new series of compact minitwistor spaces and Moishezon twistor spaces over them

On the cuspidal locus in the dual varieties of Segre quartic surface

A modified variational principle for gravity in the modified Weyl geometry

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