NORMAL FUNCTIONS FOR ALGEBRAICALLY TRIVIAL CYCLES ARE ALGEBRAIC FOR ARITHMETIC REASONS
For families of smooth complex projective varieties, we show that normal functions arising from algebraically trivial cycle classes are algebraic and defined over the field of definition of the family. In particular, the zero loci of those functions are algebraic and defined over such a field of def...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2019-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509419000343/type/journal_article |
| _version_ | 1811156178179194880 |
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| author | JEFFREY D. ACHTER SEBASTIAN CASALAINA-MARTIN CHARLES VIAL |
| author_facet | JEFFREY D. ACHTER SEBASTIAN CASALAINA-MARTIN CHARLES VIAL |
| author_sort | JEFFREY D. ACHTER |
| collection | DOAJ |
| description | For families of smooth complex projective varieties, we show that normal functions arising from algebraically trivial cycle classes are algebraic and defined over the field of definition of the family. In particular, the zero loci of those functions are algebraic and defined over such a field of definition. This proves a conjecture of Charles. |
| first_indexed | 2024-04-10T04:47:11Z |
| format | Article |
| id | doaj.art-66eebb6fb8e04d439e4afeed4034b2d9 |
| institution | Directory Open Access Journal |
| issn | 2050-5094 |
| language | English |
| last_indexed | 2024-04-10T04:47:11Z |
| publishDate | 2019-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj.art-66eebb6fb8e04d439e4afeed4034b2d92023-03-09T12:34:44ZengCambridge University PressForum of Mathematics, Sigma2050-50942019-01-01710.1017/fms.2019.34NORMAL FUNCTIONS FOR ALGEBRAICALLY TRIVIAL CYCLES ARE ALGEBRAIC FOR ARITHMETIC REASONSJEFFREY D. ACHTER0SEBASTIAN CASALAINA-MARTIN1CHARLES VIAL2Colorado State University, Department of Mathematics, Fort Collins, CO 80523, USA;University of Colorado, Department of Mathematics, Boulder, CO 80309, USA;Universität Bielefeld, Fakultät für Mathematik, Germany;For families of smooth complex projective varieties, we show that normal functions arising from algebraically trivial cycle classes are algebraic and defined over the field of definition of the family. In particular, the zero loci of those functions are algebraic and defined over such a field of definition. This proves a conjecture of Charles.https://www.cambridge.org/core/product/identifier/S2050509419000343/type/journal_article14C2514C3014D0714D1014G99 |
| spellingShingle | JEFFREY D. ACHTER SEBASTIAN CASALAINA-MARTIN CHARLES VIAL NORMAL FUNCTIONS FOR ALGEBRAICALLY TRIVIAL CYCLES ARE ALGEBRAIC FOR ARITHMETIC REASONS Forum of Mathematics, Sigma 14C25 14C30 14D07 14D10 14G99 |
| title | NORMAL FUNCTIONS FOR ALGEBRAICALLY TRIVIAL CYCLES ARE ALGEBRAIC FOR ARITHMETIC REASONS |
| title_full | NORMAL FUNCTIONS FOR ALGEBRAICALLY TRIVIAL CYCLES ARE ALGEBRAIC FOR ARITHMETIC REASONS |
| title_fullStr | NORMAL FUNCTIONS FOR ALGEBRAICALLY TRIVIAL CYCLES ARE ALGEBRAIC FOR ARITHMETIC REASONS |
| title_full_unstemmed | NORMAL FUNCTIONS FOR ALGEBRAICALLY TRIVIAL CYCLES ARE ALGEBRAIC FOR ARITHMETIC REASONS |
| title_short | NORMAL FUNCTIONS FOR ALGEBRAICALLY TRIVIAL CYCLES ARE ALGEBRAIC FOR ARITHMETIC REASONS |
| title_sort | normal functions for algebraically trivial cycles are algebraic for arithmetic reasons |
| topic | 14C25 14C30 14D07 14D10 14G99 |
| url | https://www.cambridge.org/core/product/identifier/S2050509419000343/type/journal_article |
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