Pure and Applied Mathematics Quarterly

Volume 10 (2014)

Number 1

Special Issue: In Memory of Andrey Todorov, Part 2 of 3

The space of complete quotients

Pages: 155 – 192

DOI: http://dx.doi.org/10.4310/PAMQ.2014.v10.n1.a3

Authors

Yi Hu (Department of Mathematics, University of Arizona, Tucson, Ariz., U.S.A.)

Yijun Shao (Department of Mathematics, University of Arizona, Tucson, Ariz., U.S.A.)

Abstract

We introduce complete quotients over the projective line and prove that they form smooth projective varieties. The resulting parameter spaces coincide with the varieties constructed in Y. Hu, J. Lin, and Y. Shao, “A Compactification of the Space of Algebraic Maps from $\mathbb{P}^1$ to $\mathbb{P}^n$” [HLS11] and in Y. Shao, “A compactification of the space of parametrized rational curves in Grassmannians” [Shao11]. Hence they provide modular smooth compactifications with normal crossing boundaries of the spaces of algebraic maps from the projective line to Grassmannian varieties, resolving the singularities of the boundaries of the Quot scheme compactifications.

Keywords

Quot scheme, complete quotient

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