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Let $K$ be a fan-like simplicial sphere of dimension $n-1$ such that its associated complete fan is strongly polytopal, and let $v$ be a vertex of $K$. Let $K(v)$ be the simplicial wedge complex obtained by applying the simplicial wedge operation to $K$ at $v$, and let $v_0$ and $v_1$ denote two newly created vertices of $K(v)$. In this paper, we show that there are infinitely many strongly polytopal fans $\Sigma$ over such $K(v)$'s, different from the canonical extensions, whose projected fans ${\rm Proj}_{v_i} \Sigma$ $(i=0,1)$ are also strongly polytopal. As a consequence, it can be also shown that there are infinitely many projective toric varieties over such $K(v)$'s such that toric varieties over the underlying projected complexes $K_{{\rm Proj}_{v_i} \Sigma}$ $(i=0,1)$ are also projective.
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참고문헌 (8)
참고문헌 신청
A. Bahri / 2010 / Operations on polyhedral products and a new topological construction of infinite families of toric manifolds
A. Hattori / 2003 / Theory of multi-fans / Osaka J. Math 40 (1) : 1 ~ 68
G. C. Shephard / 1971 / Spherical complexes and radial projections of polytopes / Israel J. Math 9 : 257 ~ 262
G. Ewald / 1986 / Spherical complexes and nonprojective toric varieties / Discrete Comput. Geom 1 (2) : 115 ~ 122
G. Ewald / 1996 / Combinatorial convexity and algebraic geometry / Springer
A. Hattori / 2003 / Theory of multi-fans / Osaka J. Math 40 (1) : 1 ~ 68
G. C. Shephard / 1971 / Spherical complexes and radial projections of polytopes / Israel J. Math 9 : 257 ~ 262
G. Ewald / 1986 / Spherical complexes and nonprojective toric varieties / Discrete Comput. Geom 1 (2) : 115 ~ 122
G. Ewald / 1996 / Combinatorial convexity and algebraic geometry / Springer
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