Suppose that a compact r-dimensional torus Tr 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 (d−r+1)-dimensional polarized projective orbifold Mˆν (referred to as the ν-th conic transform of M). Namely, Mˆν 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 Mˆν is itself a Kähler toric orbifold, 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, 202(August 2024) [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 Tr 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 (d−r+1)-dimensional polarized projective orbifold Mˆν (referred to as the ν-th conic transform of M). Namely, Mˆν 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 Mˆν is itself a Kähler toric orbifold, 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
Conic transform; Contact lift; Hamiltonian action; Marked moment polytope; Symplectic structure; Toric symplectic orbifold;
English
13-mag-2024
2024
202
August 2024
105224
open
Paoletti, R. (2024). The symplectic structure of a toric conic transform. JOURNAL OF GEOMETRY AND PHYSICS, 202(August 2024) [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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