Mathematics Colloquia and Seminars

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A stable n-marked curve is a nodal curve with n distinct marked points and finitely many automorphisms. If we choose rational numbers $a_1, . . ., a_n$ in the interval (0, 1], then a weighted stable n-marked curve is a generalization where the marks are allowed to coincide as long as the total weight at any point is at most one. Moduli of weighted stable curves were first constructed by Hassett. On the other hand, a twisted stable n-marked curve is a tame stack whose coarse moduli space is a stable n-marked curve, such that stacky structure is concentrated at nodes and markings and has a specific local description. I will discuss a modification (using log geometry) of the moduli of twisted stable curves where the markings are allowed to coincide, analogous to Hassett's construction for representable curves. This is a joint work-in-progress with Martin Olsson.