Birational geometry of hypersurfaces in products of projective spaces

DOI10.1007/s00209-015-1415-xzbMath1333.14013arXiv1305.0537OpenAlexW1985763187MaRDI QIDQ2349887

John Christian Ottem

Publication date: 18 June 2015

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.0537

zbMATH Keywords

birational geometryMori dream spacecox ring

Mathematics Subject Classification ID

Rational and birational maps (14E05) Minimal model program (Mori theory, extremal rays) (14E30) Hypersurfaces and algebraic geometry (14J70)

Related Items (14)

Birational automorphism groups and the movable cone theorem for Calabi-Yau complete intersections of products of projective spaces ⋮ Counterexamples of Lefschetz hyperplane type results for movable cones ⋮ Remarks on nef and movable cones of hypersurfaces in Mori dream spaces ⋮ Non-holomorphic cycles and non-BPS black branes ⋮ On the unirationality of quadric bundles ⋮ Quartic and Quintic Hypersurfaces with Dense Rational Points ⋮ Flops for complete intersection Calabi-Yau threefolds ⋮ On the birational geometry of Hilbert schemes of points and Severi divisors ⋮ Examples of Mori dream spaces with Picard number two ⋮ On birational rigidity of singular del Pezzo fibrations of degree 1 ⋮ The Lefschetz Principle in Birational Geometry: Birational Twin Varieties ⋮ Local positivity of linear series on surfaces ⋮ A Remark on Rationally Connected Varieties and Mori Dream Spaces ⋮ On weak Fano manifolds with small contractions obtained by blow-ups of a product of projective spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Examples of Mori dream spaces with Picard number two
• On pliability of del Pezzo fibrations and Cox rings
• A Lefschetz hyperplane theorem for Mori dream spaces
• The weak Lefschetz principle is false for ample cones.
• Hypersurfaces in Mori dream spaces
• Cox rings of \(K3\) surfaces with Picard number 2
• Families of hypersurfaces of large degree
• On the ample cone of an ample hypersurface
• The Noether-Lefschetz theorem for the divisor class group
• Birational automorphism groups and the movable cone theorem for Calabi-Yau manifolds of Wehler type via universal Coxeter groups
• Cox Rings
• Vector Bundles Over an Elliptic Curve
• On rational surfaces, II
• Cox rings and combinatorics II
• On the Cone of Divisors of Calabi–Yau Fiber Spaces
• Polarized Pushouts over Finite Fields
• Mori dream spaces and GIT.

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