Proceedings of the Japan Academy, Series A, Mathematical Sciences

Toric 2-Fano manifolds and extremal contractions

Hiroshi Sato

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Abstract

We show that for a projective toric manifold with the ample second Chern character, if there exists a Fano contraction, then it is isomorphic to the projective space. For the case that the second Chern character is nef, the Fano contraction gives either a projective line bundle structure or a direct product structure. We also show that, for a toric weakly 2-Fano manifold, there does not exist a divisorial contraction to a point.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 92, Number 10 (2016), 121-124.

Dates
First available in Project Euclid: 2 December 2016

Permanent link to this document
https://projecteuclid.org/euclid.pja/1480669218

Digital Object Identifier
doi:10.3792/pjaa.92.121

Mathematical Reviews number (MathSciNet)
MR3579193

Zentralblatt MATH identifier
1375.14177

Subjects
Primary: 14M25: Toric varieties, Newton polyhedra [See also 52B20]
Secondary: 14J45: Fano varieties 14E30: Minimal model program (Mori theory, extremal rays)

Keywords
Toric variety Mori theory 2-Fano manifold

Citation

Sato, Hiroshi. Toric 2-Fano manifolds and extremal contractions. Proc. Japan Acad. Ser. A Math. Sci. 92 (2016), no. 10, 121--124. doi:10.3792/pjaa.92.121. https://projecteuclid.org/euclid.pja/1480669218


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References

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