Browse Dissertations and Theses - Mathematics by Contributor "Katz, Sheldon"

• (2014-05-30)
The Hilbert scheme of $n$ points in a smooth del Pezzo surface $S$ parameterizes zero-dimensional subschemes with length $n$ on $S$. We construct a flat family of deformations of Hilb$^n S$ which can be conceptually ...

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• (2012-09-18)
This thesis consists of three parts. In the first part, we compute the topological Euler characteristics of the moduli spaces of stable sheaves of dimension one on the total space of rank 2 bundle on P1 whose determinant ...

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• (2006)
We consider the problem of constructing K3-fibered and elliptically fibered Calabi-Yau threefolds over P1 and P2 respectively. We first show how to write weighted projective space bundles as toric varieties. We then ...

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• (2017-07-10)
In this thesis we mainly consider supermanifolds and super Hilbert schemes. In the first part of this dissertation, we construct the Hilbert scheme of $0$-dimensional subspaces on dimension $1 | 1$ supermanifolds. By ...

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• (2010-08-20)
In this thesis, we first use the ${\mathbb C^*}^2$-action on the Hilbert scheme of two points on a Hirzebruch surface to compute all one-pointed and some two-pointed Gromov-Witten invariants via virtual localization, then ...

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• (2017-07-05)
Suppose $f(x,y)$ is a binary form of degree $d$ with coefficients in a field $K \subseteq \cc$. The {\it $K$-rank of $f$} is the smallest number of $d$-th powers of linear forms over $K$ of which $f$ is a $K$-linear ...

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• (2011-08-25)
This thesis is composed of two parts. In the first part we introduce a higher rank analog of the Pandharipande-Thomas theory of stable pairs on a Calabi-Yau threefold $X$. More precisely, we develop a moduli theory for ...

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