Projections of Mukai varieties
DOI:
https://doi.org/10.7146/math.scand.a-106223Abstract
This note is an answer to a problem proposed by Iliev and Ranestad. We prove that the projections of general nodal linear sections of suitable dimension of Mukai varieties Mg are linear sections of Mg−1.References
Abo, H., Ottaviani, G., and Peterson, C., Non-defectivity of Grassmannians of planes, J. Algebraic Geom. 21 (2012), no. 1, 1–20. https://doi.org/10.1090/S1056-3911-2010-00540-1
Ein, L., Varieties with small dual varieties. I, Invent. Math. 86 (1986), no. 1, 63–74. https://doi.org/10.1007/BF01391495
de Graaf, W. A., Computing with nilpotent orbits in simple Lie algebras of exceptional type, LMS J. Comput. Math. 11 (2008), 280–297. https://doi.org/10.1112/S1461157000000607
Iliev, A. and Ranestad, K., Geometry of the Lagrangian Grassmannian bfLG(3,6) with applications to Brill-Noether loci, Michigan Math. J. 53 (2005), no. 2, 383–417. https://doi.org/10.1307/mmj/1123090775
Kapustka, G., Primitive contractions of Calabi-Yau threefolds. II, J. Lond. Math. Soc. (2) 79 (2009), no. 1, 259–271. https://doi.org/10.1112/jlms/jdn069
Kapustka, M., Geometric transitions between Calabi-Yau threefolds related to Kustin-Miller unprojections, J. Geom. Phys. 61 (2011), no. 8, 1309–1318. https://doi.org/10.1016/j.geomphys.2011.02.022
Kapustka, M. and Ranestad, K., Vector bundles on Fano varieties of genus ten, Math. Ann. 356 (2013), no. 2, 439–467. https://doi.org/10.1007/s00208-012-0856-3
Knop, F. and Menzel, G., Duale Varietäten von Fahnenvarietäten, Comment. Math. Helv. 62 (1987), no. 1, 38–61. https://doi.org/10.1007/BF02564437
Landsberg, J. M. and Manivel, L., The projective geometry of Freudenthal's magic square, J. Algebra 239 (2001), no. 2, 477–512. https://doi.org/10.1006/jabr.2000.8697
Mukai, S., Curves, K3 surfaces and Fano 3-folds of genus leq10, in “Algebraic geometry and commutative algebra, Vol. I”, Kinokuniya, Tokyo, 1988, pp. 357--377.
Mukai, S., Curves and Grassmannians, in “Algebraic geometry and related topics (Inchon, 1992)'', Conf. Proc. Lecture Notes Algebraic Geom., I, Int. Press, Cambridge, MA, 1993, pp. 19--40.
Papadakis, S. A., Kustin-Miller unprojection with complexes, J. Algebraic Geom. 13 (2004), no. 2, 249–268. https://doi.org/10.1090/S1056-3911-03-00350-3
Ranestad, K., Non-abelian Brill-Noether loci and the Lagrangian Grassmannian rmLG(3,6), in “The Fano Conference”, Univ. Torino, Turin, 2004, pp. 683--692.
Ranestad, K. and Schreyer, F.-O., Varieties of sums of powers, J. Reine Angew. Math. 525 (2000), 147–181. https://doi.org/10.1515/crll.2000.064
Sato, M. and Kimura, T., A classification of irreducible prehomogeneous vector spaces and their relative invariants, Nagoya Math. J. 65 (1977), 1–155.
