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

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 Y₀ to deform to a scheme of finitely many smooth isolated curves in a general deformation Y_t of Y₀. In this part, we find two new methods to check whether the set of nodes of Y₀ 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.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Grantor dc:publisher

The Ohio State University

Year dc:date

2013

Author dc:creator

• Yu, Xun

Contributors dc:contributor

• Clemens, Herb

• Mathematics

Statement dc:rights

• unrestricted
• This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.

Language dc:language

English

Repository record dc:identifier

http://rave.ohiolink.edu/etdc/view?acc_num=osu1366208383

OAI identifier oai:identifier

oai:etd.ohiolink.edu:osu1366208383