Flattening stratification and the stack of partial stabilizations of prestable curves

Author: Kresch Andrew  

Publisher: Oxford University Press

ISSN: 0024-6093

Source: Bulletin of the London Mathematical Society, Vol.45, Iss.1, 2013-02, pp. : 93-102

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Abstract

We describe the stack of partial stabilizations of prestable curves. We use this description to obtain examples of proper morphisms of schemes having no flattening stratification and to obtain results on the existence of global quotient stack presentations in the setting of moduli stack of prestable curves of genus 0.