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Lower bounds of Tian's invariant under toric invariances

✍ Scribed by Adnène Ben Abdesselem; Malek Filali

Publisher
Elsevier Science
Year
2010
Tongue
French
Weight
154 KB
Volume
134
Category
Article
ISSN
0007-4497

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✦ Synopsis

On some toric Fano manifolds with metrics in the first Chern class, we show that a large family of smooth almost pluri-subharmonic functions (i.e. subharmonic with respect to the metric) with maximum equal to 0 admits a lower envelope. In our previous papers [4] and A. Ben Abdesselem and B. [5]) we established such envelopes when the functions considered are invariant under the action of a larger automorphisms group. Here we only consider the invariances due to the of the toric structure of the manifolds.

📜 SIMILAR VOLUMES

Invariants of real rational symplectic 4
Invariants of real rational symplectic 4-manifolds and lower bounds in real enumerative geometry
✍ Jean-Yves Welschinger 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 92 KB

Following the approach of Gromov and Witten, we construct invariants under deformation of real rational symplectic 4-manifolds. These invariants provide lower bounds for the number of real rational J -holomorphic curves in a given homology class passing through a given real configuration of points.