This thesis exhibits two of the author's works: the first is about interpreting the derived equivalences of K3 surfaces through Cremona transformations, where we construct …
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 …
We study the moduli stacks of logarithmic stable maps when the target variety X is equipped with an action of a one-dimensional torus C*. Specifically, …
We study the numerical invariants attached to families of Abelian fourfolds constructed by Mumford with extra codimension 2 Hodge cycles that are generically not endowed …
The main subject of this dissertation is the study of certain moduli spaces intimately related to the enumerative geometry of complex algebraic varieties and orbifolds. …
This thesis explores transversality between algebraic varieties and linear subspaces in the setting of finite fields. The main contributions are effective Bertini-type results for smooth …
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 …