Geometry of nondegenerate polynomials: Motivic nearby cycles and Cohomology of contact loci
We study polynomials with complex coefficients which are nondegenerate in two senses, one of Kouchnirenko and the other with respect to its Newton polyhedron, through data on contact loci and motivic nearby cycles. Introducing an explicit description of these quantities we can answer in part the que...
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Académie des sciences
2023-10-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.492/ |
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| author | Lê, Quy Thuong Nguyen, Tat Thang |
| author_facet | Lê, Quy Thuong Nguyen, Tat Thang |
| author_sort | Lê, Quy Thuong |
| collection | DOAJ |
| description | We study polynomials with complex coefficients which are nondegenerate in two senses, one of Kouchnirenko and the other with respect to its Newton polyhedron, through data on contact loci and motivic nearby cycles. Introducing an explicit description of these quantities we can answer in part the question concerning the motivic nearby cycles of restriction functions in the context of Newton nondegenerate polynomials. Furthermore, in the nondegeneracy in the sense of Kouchnirenko, we give calculations on cohomology groups of the contact loci. |
| format | Article |
| id | doaj-art-5dbd779162064b06bcffd8599b650288 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-10-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-5dbd779162064b06bcffd8599b6502882025-02-07T11:10:23ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-10-01361G81249126610.5802/crmath.49210.5802/crmath.492Geometry of nondegenerate polynomials: Motivic nearby cycles and Cohomology of contact lociLê, Quy Thuong0Nguyen, Tat Thang1Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka, 560-0043, Japan; University of Science, Vietnam National University, Hanoi, 334 Nguyen Trai Street, Thanh Xuan District, Hanoi, VietnamInstitute of Mathematics, Vietnam Academy of Science and Technology 18 Hoang Quoc Viet Road, Cau Giay District, Hanoi, VietnamWe study polynomials with complex coefficients which are nondegenerate in two senses, one of Kouchnirenko and the other with respect to its Newton polyhedron, through data on contact loci and motivic nearby cycles. Introducing an explicit description of these quantities we can answer in part the question concerning the motivic nearby cycles of restriction functions in the context of Newton nondegenerate polynomials. Furthermore, in the nondegeneracy in the sense of Kouchnirenko, we give calculations on cohomology groups of the contact loci.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.492/arc spacescontact locimotivic zeta functionmotivic Milnor fibermotivic nearby cyclesNewton polyhedronnondegeneracysheaf cohomology with compact support |
| spellingShingle | Lê, Quy Thuong Nguyen, Tat Thang Geometry of nondegenerate polynomials: Motivic nearby cycles and Cohomology of contact loci Comptes Rendus. Mathématique arc spaces contact loci motivic zeta function motivic Milnor fiber motivic nearby cycles Newton polyhedron nondegeneracy sheaf cohomology with compact support |
| title | Geometry of nondegenerate polynomials: Motivic nearby cycles and Cohomology of contact loci |
| title_full | Geometry of nondegenerate polynomials: Motivic nearby cycles and Cohomology of contact loci |
| title_fullStr | Geometry of nondegenerate polynomials: Motivic nearby cycles and Cohomology of contact loci |
| title_full_unstemmed | Geometry of nondegenerate polynomials: Motivic nearby cycles and Cohomology of contact loci |
| title_short | Geometry of nondegenerate polynomials: Motivic nearby cycles and Cohomology of contact loci |
| title_sort | geometry of nondegenerate polynomials motivic nearby cycles and cohomology of contact loci |
| topic | arc spaces contact loci motivic zeta function motivic Milnor fiber motivic nearby cycles Newton polyhedron nondegeneracy sheaf cohomology with compact support |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.492/ |
| work_keys_str_mv | AT lequythuong geometryofnondegeneratepolynomialsmotivicnearbycyclesandcohomologyofcontactloci AT nguyentatthang geometryofnondegeneratepolynomialsmotivicnearbycyclesandcohomologyofcontactloci |