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A simple proof of the non-rationality of a general quartic double solid

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The aim of this short note is to give a simple proof of the non-rationality of the double cover of the three-dimensional projective space branched over a sufficiently general quartic.

Abstract

The aim of this short note is to give a simple proof of the non-rationality of the double cover of the three-dimensional projective space branched over a sufficiently general quartic.

참고문헌 (16)

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  3. A. Beauville, "Non-rationality of the symmetric sextic Fano threefold", Geometry and arithmetic, EMS Ser. Congr. Rep., pp.57~60 (2012), Eur. Math. Soc.
  4. A. Beauville, "Non-rationality of the S6-symmetric quartic threefolds", Rend. Semin. Mat. Univ. Politec. Torino, 71(3-4), pp.385~388 (2013)
  5. I. Cheltsov, "Quartic double solids with icosahedral symmetry", Eur. J. Math, 2(1), pp.96~119 (2016)
  6. I. Cheltsov, "Which quartic double solids are rational?", J. Algebraic Geom (2015)
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  8. C. H. Clemens, "Complex geometry and Lie theory", pp.89~101 (1991), Amer. Math. Soc.
  9. C. H. Clemens, "The intermediate Jacobian of the cubic threefold", Ann. of Math. (2), 95, pp.281~356 (1972)
  10. O. Debarre, "Sur le théorème de Torelli pour les solides doubles quartiques", Compos. Math, 73(2), pp.161~187 (1990)
  11. V. Przyjalkowski, "Double quadrics with large automorphism groups", Proc. Steklov Inst. Math, 294, pp.154~175 (2016)
  12. A. S. Tikhomirov, "The Abel-Jacobi mapping of sextics of genus three onto double P3's of index two", Soviet Math. Dokl, 33(1), pp.204~206 (1986)
  13. R. Varley, "Weddle's surfaces, Humbert's curves, and a certain 4-dimensional abelian variety", Amer. J. Math, 108(4), pp.931~952 (1986)
  14. C. Voisin, "Sur la jacobienne intermédiaire du double solide d'indice deux", Duke Math. J, 57(2), pp.629~646 (1988)
  15. C. Voisin, "Unirational threefolds with no universal codimension 2 cycle", Invent. Math, 201(1), pp.207~237 (2015)
  16. Y. Zarhin, "Algebra, arithmetic, and geometry", pp.687~691 (2009), Birkhäuser

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