On a Construction of the Twistor Spaces of Joyce Metrics, Ii
نویسنده
چکیده
We explicitly construct the twistor spaces of Joyce metrics with torus action that are not treated in Part I. This finishes a construction of all the twistor spaces of Joyce metrics on the connected sum of four complex projective planes.
منابع مشابه
Projective Models of the Twistor Spaces of Joyce Metrics
We provide a simple algebraic construction of the twistor spaces of arbitrary Joyce’s self-dual metrics on the 4-manifold H 2 × T 2 that extend smoothly to nCP, the connected sum of complex projective planes. Indeed, we explicitly realize projective models of the twistor spaces of arbitrary Joyce metrics on nCP in a CP-bundle over CP, and show that they contain the twistor spaces of H 2 × T 2 a...
متن کاملOn a Construction of the Twistor Spaces of Joyce Metrics
We explicitly construct the twistor spaces of some self-dual metrics with torus action given by D. Joyce. Starting from a fiber space whose fibers are compact singular toric surfaces, we apply a number of birational transformations to obtain the desired twistor spaces. Especially an important role is played by flops, a useful operation in algebraic geometry.
متن کاملOn a Construction of the Twistor Spaces of Joyce Metrics, I
We explicitly construct the twistor spaces of some self-dual metrics with torus action given by D. Joyce. Starting from a fiber space over a projective line whose fibers are compact singular toric surfaces, we apply a number of birational transformations to obtain the desired twistor spaces. Especially an important role is played by Atiyah’s flop.
متن کاملA New Series of Compact Minitwistor Spaces and Moishezon Twistor Spaces over Them
In recent papers [8, 9], we gave explicit description of some new Moishezon twistor spaces. In this paper, generalizing the method in the papers, 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...
متن کاملToric Anti-self-dual Einstein Metrics via Complex Geometry
Using the twistor correspondence, we give a classification of toric anti-self-dual Einstein metrics: each such metric is essentially determined by an odd holomorphic function. This explains how the Einstein metrics fit into the classification of general toric anti-self-dual metrics given in an earlier paper [7]. The results complement the work of Calderbank–Pedersen [6], who describe where the ...
متن کامل