Deformations of Generalized Kahler Structures and Bihermitian Structures

Details Deformations of Generalized Kahler Structures and Bihermitian Structures Deformations of Generalized Kahler Structures and Bihermitian Structures

2009-10-09

arxiv.org/abs/0910.1651v1

Mathematics

Differential Geometry

39 pages

Scientific paper

Let $(X, J)$ be a compact Kahler manifold with a non-zero holomorphic Poisson structure $\beta$. If the obstruction space for deformations of generalized complex structures on $(X, J)$ vanishes, we obtain a family of deformations of non-trivial bihermitian structures $(J, J^-_t, h_t)$ on $X$ by using $\beta$. In addition, if the class $[\beta\cdot \omega]$ does not vanish for a K\"ahler form $\omega$, then the complex structure $J_t^-$ is not equivalent to $J$ for small $t\neq 0$ under diffeomorphisms. Our method is based on the construction of generalized complex and Kahler structures developed in \cite{Go1} and \cite{Go2}. As applications, we obtain such deformations of bihermitian structures on del Pezzo surfaces, the Hirtzebruch surfaces $F_2, F_3$ and degenerate del Pezzo surfaces. Further we show that del Pezzo surfaces $S_n (5\leq n\leq 8)$, $F_2$ and degenerate del Pezzo surfaces admit bihermitian structures for which $(X, J^-_t)$ is not biholomorphic to $(X, J)$ for small $t\neq 0$.

Affiliated with

Also associated with

No associations

Rating

Deformations of Generalized Kahler Structures and Bihermitian Structures does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Deformations of Generalized Kahler Structures and Bihermitian Structures, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Deformations of Generalized Kahler Structures and Bihermitian Structures will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-50758