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Birational Geometry of the Space of Complete Quadrics
Let $X$ be the moduli space of complete $(n-1)$-quadrics. In this thesis, we study the birational geometry of $X$ using tools from the minimal model program (MMP). In Chapter $1$, we recall the definition of the space $X$ ...
The Effective Cone of Moduli Spaces of Sheaves on a Smooth Quadric Surface
In this paper, we provide an approach to computing the effective cone of moduli spaces of sheaves on a smooth quadric surface. We find Brill-Noether divisors spanning extremal rays of the effective cone using resolutions ...
Effective Divisors on Kontsevich Moduli Spaces
We study the cone of effective divisors on Kontsevich's moduli space of genus 0 stable maps to projective space in the case where map is equipped with a marked point on the domain curve, extending previous work of Coskun, ...