Thời gian: 16h30, thứ Năm, 10/10/2024

Tóm tắt: To study the invariance of higher Nash blowup local algebra, it is important to work on higher Nash blowups and higher Jacobian ideals of regular functions. Given a positive integer n, to a morphism of varieties X to S one associates the sheaf of Kähler differentials of order n. Based on the work of Oneto-Zatini (1991), the sheaf yields the n-th Nash blowup of X. This topic, where X and S are special varieties, has been studied by many authors: Yasuda (2007, 2009), Duarte (2014, 2017), Brenner-Jeffries-Nunez-Betancourt (2019), Toh-Yama (2019), Barajas-Duarte (2020), de Alba-Duarte (2021), and so on. According to the work of Oneto-Zatini and Villamayor, the n-th Nash blowup of X is isomorphic to the blowup of X with the center a certain fractional ideal of the sheaf of total quotient rings of X. In this talk, we consider X to be smooth and S to be the affine line A, and in this case, we can choose this fractional ideal as a certain Fitting ideal of the sheaf of Kähler differentials of order n, called the n-th Jacobian of X/A. By studying this ideal, we prove a stronger version of Hussain-Ma-Yau-Zuo's conjecture that higher Nash blowup local algebras are invariant under contact equivalence (over C).

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