Toric Symplectic Singular Spaces I: Isolated Singularities
نویسنده
چکیده
We generalize a theorem of Delzant classifying compact connected symplectic manifolds with completely integrable torus actions to certain singular symplectic spaces. The assumption on singularities is that if they are not finite quotient then they are isolated.
منابع مشابه
Questions about cobordism of symplectic and toric manifolds
1 Toric varieties are by now familiar objects in algebraic geometry, but this note is concerned with variations on that theme, and I will try to be careful about terminology. A toric variety is a kind of orbifold, and hence has mild singularities, but I will use the term toric manifold in the sense of Davis and Januszkiewicz [4]; a smooth toric variety thus has an underlying toric manifold, but...
متن کاملSymplectic Toric Manifolds
Foreword These notes cover a short course on symplectic toric manifolds, delivered in six lectures at the summer school on Symplectic Geometry of Integrable Hamiltonian Systems, mostly for graduate students, held at the Centre de Recerca Matemàtica in Barcelona in July of 2001. The goal of this course is to provide a fast elementary introduction to toric manifolds (i.e., smooth toric varieties)...
متن کاملPoisson traces, D-modules, and symplectic resolutions
We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a ...
متن کاملLog geometry and multiplier ideals
I work in combinatorics, algebraic geometry, convex geometry and commutative algebra while staying informed on certain topics in category theory and ring theory. In particular, I focus on toric varieties and singularity theory. The study of toric varieties lies at the intersection of combinatorics, algebraic geometry, convex geometry and integer programming. There is a correspondence between ce...
متن کاملGlobal classification of curves on the symplectic plane
In [17], we considered the local classification of plane curves on the symplectic plane. In particular, we introduced the number “symplectic defect”, which represents the difference of two natural equivalence relations on plane curves, the equivalence by diffeomorphisms and that by symplectomorphisms. For an immersion, two equivalence relations coincide, so the symplectic defect is null. For co...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008