Suppose that a compact r-dimensional torus acts in a holomorphic and Hamiltonian manner on polarized complex d-dimensional projective manifold M, with nowhere vanishing moment map Φ. Assuming that Φ is transverse to the ray through a given weight ν, associated to these data there is a complex -dimensional polarized projective orbifold (referred to as the ν-th conic transform of M). Namely, is a suitable quotient of the inverse image of the ray in the unit circle bundle of the polarization of M. With the aim to clarify the geometric significance of this construction, we consider the special case where M is toric, and show that is itself a Kähler toric obifold, whose (marked) moment polytope is obtained from the one of M by a certain ‘transform’ operation (depending on Φ and ν).

Paoletti, R. (2024). The symplectic structure of a toric conic transform. JOURNAL OF GEOMETRY AND PHYSICS [10.1016/j.geomphys.2024.105224].

The symplectic structure of a toric conic transform

Paoletti, R
2024

Abstract

Suppose that a compact r-dimensional torus acts in a holomorphic and Hamiltonian manner on polarized complex d-dimensional projective manifold M, with nowhere vanishing moment map Φ. Assuming that Φ is transverse to the ray through a given weight ν, associated to these data there is a complex -dimensional polarized projective orbifold (referred to as the ν-th conic transform of M). Namely, is a suitable quotient of the inverse image of the ray in the unit circle bundle of the polarization of M. With the aim to clarify the geometric significance of this construction, we consider the special case where M is toric, and show that is itself a Kähler toric obifold, whose (marked) moment polytope is obtained from the one of M by a certain ‘transform’ operation (depending on Φ and ν).
Articolo in rivista - Articolo scientifico
Toric orbifold; Hamiltonian action; unit circle bundle; contact lift; marked moment polytope; symplectic structure; conic transform
English
13-mag-2024
2024
none
Paoletti, R. (2024). The symplectic structure of a toric conic transform. JOURNAL OF GEOMETRY AND PHYSICS [10.1016/j.geomphys.2024.105224].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/476259
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