Comptes Rendus
Géométrie algébrique, Géométrie et Topologie
Geometry of nondegenerate polynomials: Motivic nearby cycles and Cohomology of contact loci
Quy Thuong Lê1, 2 ; Tat Thang Nguyen3 
1 University of Science, Vietnam National University, Hanoi, 334 Nguyen Trai Street, Thanh Xuan District, Hanoi, Vietnam
2 Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka, 560-0043, Japan
3 Institute of Mathematics, Vietnam Academy of Science and Technology 18 Hoang Quoc Viet Road, Cau Giay District, Hanoi, Vietnam
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1249-1266.

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.

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DOI : 10.5802/crmath.492
Classification : 14B05, 14B07, 14J17, 32S05, 32S30, 32S55
Mots clés : arc spaces, contact loci, motivic zeta function, motivic Milnor fiber, motivic nearby cycles, Newton polyhedron, nondegeneracy, sheaf cohomology with compact support
Quy Thuong Lê 1, 2 ; Tat Thang Nguyen 3

1 University of Science, Vietnam National University, Hanoi, 334 Nguyen Trai Street, Thanh Xuan District, Hanoi, Vietnam
2 Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka, 560-0043, Japan
3 Institute of Mathematics, Vietnam Academy of Science and Technology 18 Hoang Quoc Viet Road, Cau Giay District, Hanoi, Vietnam
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     journal = {Comptes Rendus. Math\'ematique},
     pages = {1249--1266},
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     language = {en},
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Quy Thuong Lê; Tat Thang Nguyen. Geometry of nondegenerate polynomials: Motivic nearby cycles and Cohomology of contact loci. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1249-1266. doi : 10.5802/crmath.492. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.492/

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