Twistors, quartics, and del Pezzo fibrations / Nobuhiro Honda.

Format:

Book

Author/Creator:

Honda, Nobuhiro, author.

Series:

Memoirs of the American Mathematical Society ; no. 1414.

Memoirs of the American Mathematical Society, 0065-9266 ; number 1414

Language:

English

Subjects (All):

Geometry, Differential.

Geometry, Algebraic.

Quartic surfaces.

Twistor theory.

Physical Description:

vii, 134 pages : illustrations ; 26 cm

Place of Publication:

Providence, RI : American Mathematical Society, 2023.

Summary:

"It has been known that twistor spaces associated to self-dual metrics on compact 4-manifolds are source of interesting examples of non-projective Moishezon threefolds. In this paper we investigate the structure of a variety of new Moishezon twistor spaces. The anti-canonical line bundle on any twistor space admits a canonical half, and we analyze the structure of twistor spaces by using the plurihalf- anti-canonical map from the twistor spaces. Specifically, each of the present twistor spaces is bimeromorphic to a double covering of a scroll of planes over a rational normal curve, and the branch divisor of the double cover is a cut of the scroll by a quartic hypersurface. In particular, the double covering has a pencil of Del Pezzo surfaces of degree two. Correspondingly, the twistor spaces have a pencil of rational surfaces with big anti-canonical class. The base locus of the last pencil is a cycle of rational curves, and it is an anticanonical curve on smooth members of the pencil. These twistor spaces are naturally classified into four types according to the type of singularities of the branch divisor, or equivalently, those of the Del Pezzo surfaces in the pencil. We also show that the quartic hypersurface satisfies a strong constraint and as a result the defining polynomial of the quartic hypersurface has to be of a specific form. Together with our previous result in [13], the present result completes a classification of Moishezon twistor spaces whose half-anti-canonical system is a pencil. Twistor spaces whose half-anti-canonical system is larger than pencil have been understood for a long time before. In the opposite direction, no example is known of a Moishezon twistor space whose half-anti-canonical system is smaller than a pencil. Twistor spaces which have a similar structure were studied in [12] and [16], and they are very special examples among the present twistor spaces"-- Provided by publisher.

Contents:

Moishezon twistor spaces and the fundamental system

Study on the pluri-system |lF| via relativization

Study on the direct image sheaf

Existence of real reducible members of |mF|

Description of the twistor spaces by quartic polynomials.

Notes:

Includes bibliographical references.

ISBN:

9781470464127

1470464128

OCLC:

1381796332