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Hội thảo sắp diễn ra
Gặp gỡ Toán học 2025 - Hội thảo Khoa học các nhà nghiên cứu trẻ"
Lectures on selected areas in Pure Mathematics
Hội nghị toàn quốc lần thứ VII “Xác suất - Thống kê: Nghiên cứu, ứng dụng và giảng dạy”
Xuất bản mới
Polynomial functors, wreath products and pointed admissible G-covers.
Người báo cáo: Fabio Perroni (University of Trieste)
Time: 9:00 - 10h30, 12rd June
Venue: Room 507, A6, Institute of Mathematics
Abstract: I will report on a work in progress aimed at determining recursive formulae for the Betti numbers of the moduli space of admissible G-covers of genus zero curves, where G is a finite group. We follow the approach of Getzler-Kapranov and of Manin to compute the Betti numbers of the moduli space of pointed curves of genus zero (which corresponds to the case where G is the trivial group), using the theory of operads.
For a general G, following Macdonald article “Polynomial functors and wreath products”, we define a composition operation on the Grothendieck group of varieties and we show that the Hodge-Grothendieck characteristic can be used to express the Betti numbers of the moduli space in terms of those of the loci corresponding to covering of the projective line.