On Algebraic Cycles on Fibre Products of Non-isotrivial Families of Regular Surfaces with Geometric Genus 1
Let ) be a projective family of surfaces (possibly with degenerations) over a smooth projective curve . Assume that the discriminant loci are disjoint, for any smooth fibre and the period map associated with the variation of Hodge structures (where is a s...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2016-08-01
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| Series: | Моделирование и анализ информационных систем |
| Subjects: | |
| Online Access: | https://www.mais-journal.ru/jour/article/view/370 |
| Summary: | Let ) be a projective family of surfaces (possibly with degenerations) over a smooth projective curve . Assume that the discriminant loci are disjoint, for any smooth fibre and the period map associated with the variation of Hodge structures (where is a smooth part of the morphism ), is non-constant. If for generic geometric fibres and the following conditions hold: (i) is an odd integer; (ii) , then for any smooth projective model of the fibre product the Hodge conjecture on algebraic cycles is true. If, besides, the morphisms are smooth, are odd prime numbers and , then for |
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| ISSN: | 1818-1015 2313-5417 |