We prove a weak factorization result on birational maps of Deligne-Mumford stacks, and deduce the following: Let $U \subset X$ be an open embedding of …
While the study of algebraic curves and their moduli has been a celebrated subject in algebraic and arithmetic geometry, generalizations of many results that hold …
This thesis focuses on weighted blow-ups. Weighted blow-ups are an important class of birational transformations, which has, for stacks, a similar role to the one …
Hironaka showed in his 1964 groundbreaking work that singularities of algebraic varieties admit a resolution in characteristic zero. Over the years, the proof of Hironaka’s …
Faltings's theorem states that a smooth geometrically irreducible projective curve of genus at least two defined over a number field has finitely many rational points. …
Hassett constructed a family of modular compactifications of the moduli space of pointed curves by introducing rational weights to the marked points, and proved that …