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Toric Fano manifolds with large Picard number | | Benjamin Assarf
; Benjamin Nill
; | | Date: |
25 Sep 2014 | | Abstract: | Casagrande showed that any toric Fano $d$-fold has Picard number at most
$2d$. The equality case is only attained by products of $S_3$, where $S_3$
denotes the projective plane blown up in three torus-invariant points. Toric
Fano $d$-folds with Picard number equal to $2d-1$ or $2d-2$ have been
completely classified in every dimension. In this paper, we show that for any
fixed $k$ there is only a finite number of isomorphism classes of toric Fano
$d$-folds $X$ (for arbitrary $d$) with Picard number $2d-k$ such that $X$ is
not a product of $S_3$ and a lower-dimensional toric Fano manifold. This
verifies the qualitative part of a conjecture in a recent paper by the first
author, Joswig, and Paffenholz. | | Source: | arXiv, 1409.7303 | | Services: | Forum | Review | PDF | Favorites | |
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