Higher Fano manifolds
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Carolina Araujo [6] ; Roya Beheshti [1] ; Ana-Maria Castravet [7] ; Kelly Jabbusch [2] ; Svetlana Makarova [3] ; Libby Taylor [4] ; Nivedita Viswanathan [5]
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[1] Washington University in St. Louis
Washington University in St. Louis
Estados Unidos
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[2] University of Michigan–Dearborn
University of Michigan–Dearborn
City of Dearborn, Estados Unidos
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[3] University of Pennsylvania
University of Pennsylvania
City of Philadelphia, Estados Unidos
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[4] Stanford University
Stanford University
Estados Unidos
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[5] University of Edinburgh
University of Edinburgh
Reino Unido
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[6] IMPA, Brazil
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[7] Universit´e Paris-Saclay, France
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- Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 64, Nº. Extra 1, 2022, págs. 103-125
- Idioma: inglés
- Enlaces
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Resumen
We address in this paper Fano manifolds with positive higher Chern characters, which are expected to enjoy stronger versions of several of the nice properties of Fano manifolds. For instance, they should be covered by higher dimensional rational varieties, and families of higher Fano manifolds over higher dimensional bases should admit meromorphic sections (modulo the Brauer obstruction). Aiming at finding new examples of higher Fano manifolds, we investigate positivity of higher Chern characters of rational homogeneous spaces. We determine which rational homogeneous spaces of Picard rank 1 have positive second Chern character, and show that the only rational homogeneous spaces of Picard rank 1 having positive second and third Chern characters are projective spaces and quadric hypersurfaces. We also classify Fano manifolds of large index having positive second and third Chern characters. We conclude by discussing conjectural characterizations of projective spaces and complete intersections in terms of these higher Fano conditions
