hypersurface associated to a quasi-smooth intersection subvariety X = X f 1 ‚à© ‚ãÖ ‚ãÖ ‚ãÖ ‚à© X f s ‚äÇ P d Œ£ such that d + s = 2 ( k + 1 ) . If the Hodge conjecture holds on X then it holds as well on Y .\n\nCorollary 5.4. If the dimension of Y is 2 s ‚àí 1 , 2 s or 2 s + 1 then the Hodge conjecture holds on Y .\n\nProof. By Proposition 5.3 and Corollary 3.6.\n\n[\n\n] Angella, D. Cohomologies of certain orbifolds. Journal of Geometry and Physics\n\n(\n\n),\n\n‚Äì\n\n[\n\n] Batyrev, V. V., and Cox, D. A. On the Hodge structure of projective hypersur- faces in toric varieties. Duke Mathematical Journal\n\n,\n\n(Aug\n\n). [\n\n] Bruzzo, U., and Montoya, W. On the Hodge conjecture for quasi-smooth in- tersections in toric varieties. SÀúao Paulo J. Math. Sci. Special Section: Geometry in Algebra and Algebra in Geometry (\n\n). [\n\n] Caramello Jr, F. C. Introduction to orbifolds. a\n\niv:\n\nv\n\n(\n\n). [\n\n] Cox, D., Little, J., and Schenck, H. Toric varieties, vol.\n\nAmerican Math- ematical Soc.,\n\n[\n\n] Griffiths, P., and Harris, J. Principles of Algebraic Geometry. John Wiley & Sons, Ltd,\n\n[\n\n] Mavlyutov, A. R. Cohomology of complete intersections in toric varieties. Pub- lished in PaciÔ¨Åc J. of Math.\n\nNo.\n\n(\n\n),\n\n‚Äì\n\n[\n\n] Satake, I. On a Generalization of the Notion of Manifold. Proceedings of the National Academy of Sciences of the United States of America\n\n,\n\n(\n\n),\n\n‚Äì\n\n[\n\n] Steenbrink, J. H. M. Intersection form for quasi-homogeneous singularities. Com- positio Mathematica\n\n,\n\n(\n\n),\n\n‚Äì\n\n[\n\n] Voisin, C. Hodge Theory and Complex Algebraic Geometry I, vol.\n\nof Cambridge Studies in Advanced Mathematics . Cambridge University Press,\n\n[\n\n] Wang, Z. Z., and Zaffran, D. A remark on the Hard Lefschetz theorem for K¬®ahler orbifolds. Proceedings of the American Mathematical Society\n\n,\n\n(Aug\n\n).\n\n[2] Batyrev, V. V., and Cox, D. A. On the Hodge structure of projective hypersur- faces in toric varieties.
Portable Document Format (PDF), standardized as ISO 32000, is a file format developed by Adobe in 1992 to present documents, including text formatting and images, in a manner independent of application software, hardware, and operating systems.
Portable Document Format (PDF), standardized as ISO 32000, is a file format developed by Adobe in 1992 to present documents, including text formatting and images, in a manner independent of application software, hardware, and operating systems. ->: hypersurface associated to a quasi-smooth intersection subvariety X = X f 1 ‚à© ‚ãÖ ‚ãÖ ‚ãÖ ‚à© X f s ‚äÇ P d Œ£ such that d + s = 2 ( k + 1 ) . If the Hodge conjecture holds on X then it holds as well on Y .\n\nCorollary 5.4. If the dimension of Y is 2 s ‚àí 1 , 2 s or 2 s + 1 then the Hodge conjecture holds on Y .\n\nProof. By Proposition 5.3 and Corollary 3.6.\n\n[\n\n] Angella, D. Cohomologies of certain orbifolds. Journal of Geometry and Physics\n\n(\n\n),\n\n‚Äì\n\n[\n\n] Batyrev, V. V., and Cox, D. A. On the Hodge structure of projective hypersur- faces in toric varieties. Duke Mathematical Journal\n\n,\n\n(Aug\n\n). [\n\n] Bruzzo, U., and Montoya, W. On the Hodge conjecture for quasi-smooth in- tersections in toric varieties. SÀúao Paulo J. Math. Sci. Special Section: Geometry in Algebra and Algebra in Geometry (\n\n). [\n\n] Caramello Jr, F. C. Introduction to orbifolds. a\n\niv:\n\nv\n\n(\n\n). [\n\n] Cox, D., Little, J., and Schenck, H. Toric varieties, vol.\n\nAmerican Math- ematical Soc.,\n\n[\n\n] Griffiths, P., and Harris, J. Principles of Algebraic Geometry. John Wiley & Sons, Ltd,\n\n[\n\n] Mavlyutov, A. R. Cohomology of complete intersections in toric varieties. Pub- lished in PaciÔ¨Åc J. of Math.\n\nNo.\n\n(\n\n),\n\n‚Äì\n\n[\n\n] Satake, I. On a Generalization of the Notion of Manifold. Proceedings of the National Academy of Sciences of the United States of America\n\n,\n\n(\n\n),\n\n‚Äì\n\n[\n\n] Steenbrink, J. H. M. Intersection form for quasi-homogeneous singularities. Com- positio Mathematica\n\n,\n\n(\n\n),\n\n‚Äì\n\n[\n\n] Voisin, C. Hodge Theory and Complex Algebraic Geometry I, vol.\n\nof Cambridge Studies in Advanced Mathematics . Cambridge University Press,\n\n[\n\n] Wang, Z. Z., and Zaffran, D. A remark on the Hard Lefschetz theorem for K¬®ahler orbifolds. Proceedings of the American Mathematical Society\n\n,\n\n(Aug\n\n).\n\n[2] Batyrev, V. V., and Cox, D. A. On the Hodge structure of projective hypersur- faces in toric varieties.