Geodesic
Nonrational Complete Intersections
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic geometry: Methods, relations, and applications, Tome 246 (2004), pp. 316-320

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The nonrationality of a general complete intersection $\bigcap_{i=1}^kF_i\subset{\mathbb P}^M$, where $F_i$ is a hypersurface of degree $d_i$, is proved under the condition that equality $\sum_{i=1}^kd_i=M$ holds and $\exists\,d_j\notin\{2,3,5\}$. 
@article{TM_2004_246_a21,
     author = {I. A. Cheltsov and L. Votslav},
     title = {Nonrational {Complete} {Intersections}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {316--320},
     publisher = {mathdoc},
     volume = {246},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2004_246_a21/}
}
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I. A. Cheltsov; L. Votslav. Nonrational Complete Intersections. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic geometry: Methods, relations, and applications, Tome 246 (2004), pp. 316-320. http://geodesic.mathdoc.fr/item/TM_2004_246_a21/