Some irrational quartic threefolds

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참고문헌 (30)

1. V. A. Alekseev, "On conditions for the rationality of three-folds with a pencil of del Pezzo surfaces of degree 4", Mat. Zametki, 41(5), pp.766~ (1987)
2. A. Beauville, "Varietes de Prym et jacobiennes intermediaires", Ann. Sci. Ecole Norm, 10(3), pp.309~391 (1977)
3. I. Cheltsov, "On factoriality of nodal threefolds", J. Algebraic Geom, 14(4), pp.663~690 (2005)[DOI]
4. I. Cheltsov, "Nonrational nodal quartic threefolds", Pacific J. Math, 226(1), pp.65~81 (2006)[DOI]
5. I. Cheltsov, "Factorial threefold hypersurfaces", J. Algebraic Geom, 19(4), pp.781~791 (2010)[DOI]
6. I. Cheltsov, "Factorial hypersurfaces in P 4 with nodes", Geom. Dedicata, 121, pp.205~219 (2006)[DOI]
7. A. Corti, "Factoring birational maps of threefolds after Sarkisov", J. Algebraic Geom, 4(2), pp.223~254 (1995)
8. A. Corti, "Singularities of linear systems and 3-fold birational geometry, in Explicit birational geometry of 3-folds", pp.259~312 (2000), Cambridge Univ. Press
9. S. Cynk, "Defect of a nodal hypersurface", Manuscripta Math, 104(3), pp.325~331 (2001)[DOI]
10. C. Herbert Clemens, "The Intermediate Jacobian of the Cubic Threefold", The Annals of Mathematics, 95(2), pp.281~ (1972), JSTOR[DOI]
11. D. Eisenbud, "On Varieties of minimal degree", Proceedings of Symposia in Pure Math, 46 (1987)
12. A. J. de Jong, "On the Burkhardt quartic", Math. Ann, 286(1-3), pp.309~328 (1990)[DOI]
13. A. Dimca, "Betti numbers of hypersurfaces and defects of linear systems", Duke Math. J, 60(1), pp.285~298 (1990)[DOI]
14. D. Eisenbud, "Higher Castelnuovo theory", Asterisque, (218), pp.187~202 (1993)
15. R. Friedman, "Simultaneous resolution of threefold double points", Math. Ann, 274(4), pp.671~689 (1986)[DOI]
16. R. Hartshorne, "Ample subvarieties of algebraic varieties", Lecture Notes in Mathematics, 156 (1970), Springer-Verlag
17. K. Hong, "Nonrationality of nodal quartic threefolds", Pacific J. Math, 266(1), pp.31~42 (2013)[DOI]
18. V. A. Iskovskih, "Three-dimensional quartics and counterexamples to the Luroth problem", Mat. Sb. (N. S.), 86(128), pp.140~166 (1971)
19. V. A. Iskovskikh, "Fano varieties, in Algebraic geometry", Encyclopaedia Math. Sci., 47 (1999)
20. A. -S. Kaloghiros, "The defect of Fano 3-folds", J. Algebraic Geom, 20(1), pp.127~149 (2011)[DOI]
21. A. -S. Kaloghiros, "A classification of terminal quartic 3-folds and applications to ratio"nality questions", Math. Ann, 354(1), pp.263~296 (2012)[DOI]
22. R. Kloosterman, "Maximal families of nodal varieties with defect", arXiv:1310.0227v4, ~
23. D. Kosta, "Factoriality condition of some nodal threefolds in P 4", Manuscripta Math, 127(2), pp.151~166 (2008)[DOI]
24. M. Mella, "Birational geometry of quartic 3-folds. II. The importance of being Q-factorial", Math. Ann, 330(1), pp.107~126 (2004)[DOI]
25. A. V. Pukhlikov, "Birational automorphisms of three-dimensional algebraic varieties with a pencil of del Pezzo surfaces", Izv. Math, 62(1), pp.123~164 (1998)[DOI]
26. V. G. Sarkisov, "Birational automorphisms of conic bundles", Izv. Akad. Nauk SSSR Ser. Mat, 44(4), pp.974~ (1980)
27. V. V. Shokurov, "Prym varieties : theory and applications", Izv. Akad. Nauk SSSR Ser. Mat, 47(4), pp.785~855 (1983)
28. K. A. Shramov, "Q-factorial quartic threefolds", Sb. Math, 198(7-8), pp.103~114 (2007)[DOI]
29. A. N. Tyurin, "The middle Jacobian of three-dimensional varieties", J. Soviet Math, 13, pp.707~745 (1980)
30. A. N. Varchenko, "Semicontinuity of the spectrum and an upper bound for the number of singular points of the projective hypersurface", Dokl. Akad. Nauk SSSR, 270(6), pp.1294~1297 (1983)

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