Abstract
Given a polynomial with real coefficients, we produce a motivic analog of a simple identity that relates the complex conjugation and the monodromy of the Milnor fibre of its complexification. To that purpose, we introduce motivic zeta functions that take into account complex conjugation and monodromy.
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References
A’Campo N.: Monodromy of real isolated singularities. Topology 42(6), 1229–1240 (2003)
Bochnak J., Coste M., Roy M.-F.: Real algebraic geometry. Springer-Verlag, Berlin (1998)
Deligne P.: Théorie de Hodge III. Inst. Hautes tudes Sci. Publ. Math. 44, 5–77 (1974)
Denef J., Loeser F.: Motivic Igusa zeta functions. J. Algebraic Geom. 7(3), 505–537 (1998)
Denef J., Loeser F.: Germs of arcs on singular algebraic varieties and motivic integration. Invent. math. 135, 201–232 (1999)
Dimca A., Paunescu L.: Real singularities and dihedral representations. Mat. Contemp. 12, 67–82 (1997)
Ebeling, W.: Monodromy, singularities and computer algebra, London mathematical society lecture note series, vol. 324, pp. 129–155. Cambridge University Press, Cambridge (2006)
Fichou G.: Motivic invariants of arc-symmetric sets and blow-nash equivalence. Compos. Math. 141, 655–688 (2005)
Gusein-Zade S.: The index of a singular point of a gradient vector field. Funktsional. Anal. i Prilozhen. 18(1), 7–12 (1984)
Hartshorne R.: Algebraic geometry graduate texts in math vol. 52. Springer Verlag, Berlin (1977)
Koike S., Parusiński A.: Motivic-type invariants of blow-analytic equivalence. Ann. Inst. Fourier (Grenoble) 53(7), 2061–2104 (2003)
McCrory C., Parusiński A.: Topology of real algebraic sets of dimension 4: necessary conditions. Topology 39(3), 495–523 (2000)
McCrory C., Parusiński A.: Virtual betti numbers of real algebraic varieties. C. R. Math. Acad. Sci. Paris 336(9), 763–768 (2003)
Peters, C.A.M., Steenbrink, J.H.M.: Hodge number polynomials for nearby and vanishing cohomology algebraic cycles and motives. Selected papers from the EAGER conference, vol. 2, London Mathematical Society Lecture Note Series, vol. 344, pp. 289–303. Cambridge University Press, Cambridge (2007)
Peters C.A.M., Steenbrink J.H.M.: Mixed hodge structures. Springer-Verlag, Berlin (2008)
Silhol R.: Real algebraic surfaces, lecture notes in mathematics, vol. 1392. Springer-Verlag, Berlin (1989)
Sullivan, D.: Combinatorial invariants of analytic spaces. In: Proceedings of Liverpool Singularities Symposium I, pp. 165–168. Springer, Berlin (1969/70)