Fano Varieties in Mori Fibre Spaces
Copyright policy )Fano Varieties in Mori Fibre Spaces
We show that being a general fibre of a Mori fibre space is a rather restrictive condition for a Fano variety. More specifically, we obtain two criteria (one sufficient and one necessary) for a Q-factorial Fano variety with terminal singularities to be realised as a fibre of a Mori fibre space, which turn into a characterisation in the rigid case. We apply our criteria to figure out this property up to dimension three and on rational homogeneous spaces. The smooth toric case is studied and an interesting connection with K-semistability is also investigated.
32 pages. Results on threefolds and rational homogeneous spaces strengthened. Result on toric varieties corrected. To appear in IMRN
- University of Milan Italy
- University of California, Santa Barbara United States
- Massachusetts Institute of Technology United States
- University of Cambridge United Kingdom
- University of Rome Tor Vergata Italy
Fano varieties, Mori fiber spaces, Minimal Model Program, Settore MAT/03 - GEOMETRIA, 14E30 14J45 14J26 14J30 14M25 14M15, TORIC VARIETIES; MANIFOLDS; CLASSIFICATION; DEFORMATIONS; SURFACES; GEOMETRY; CONE, [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], 4904 Pure Mathematics, Mathematics - Algebraic Geometry, 49 Mathematical Sciences, FOS: Mathematics, Mathematics (all), QA, Algebraic Geometry (math.AG)
Fano varieties, Mori fiber spaces, Minimal Model Program, Settore MAT/03 - GEOMETRIA, 14E30 14J45 14J26 14J30 14M25 14M15, TORIC VARIETIES; MANIFOLDS; CLASSIFICATION; DEFORMATIONS; SURFACES; GEOMETRY; CONE, [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], 4904 Pure Mathematics, Mathematics - Algebraic Geometry, 49 Mathematical Sciences, FOS: Mathematics, Mathematics (all), QA, Algebraic Geometry (math.AG)
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