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On Smooth Isolated Curves in General Complete Intersection Calabi-Yau Threefolds
Yu, Xun

, Doctor of Philosophy, Ohio State University, Mathematics.
This dissertation studies existence/non-existence of smooth and isolated curves in general complete intersection Calabi-Yau (CICY) threefolds. There are three parts.

In the first part, we use Knutsen's technique to prove some existence results on smooth isolated curves in general CICY threefolds. Recently Knutsen found criteria for the curves in a complete linear system $|\mathcal{L}|$ on a smooth surface $X$ in a nodal K-trivial threefold $Y_0$ to deform to a scheme of finitely many smooth isolated curves in a general deformation $Y_t$ of $Y_0$. In this part, we find two new methods to check whether the set of nodes of $Y_0$ imposes independent conditions on $|\mathcal{L}|$. As an application, we find many new examples of smooth isolated curves in general CICY threefolds.

In the second part, we prove certain non-existence results on smooth isolated curves in general quintic threefolds by using Castelnuovo theory.

In the last part, inspired by existence/non-existence results on smooth isolated curves in general CICY threefolds known so far, we make two conjectures on smooth isolated curves in general CICY threefolds.
Herb Clemens (Advisor)

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Yu, Xun. "On Smooth Isolated Curves in General Complete Intersection Calabi-Yau Threefolds." Electronic Thesis or Dissertation. Ohio State University, . OhioLINK Electronic Theses and Dissertations Center. 26 Sep 2017.

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Yu, Xun "On Smooth Isolated Curves in General Complete Intersection Calabi-Yau Threefolds." Electronic Thesis or Dissertation. Ohio State University, . https://etd.ohiolink.edu/

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