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theses

We construct projective moduli spaces of semistable objects on an Enriques surface for generic Bridgeland stability condition. On the way, we prove the non-emptiness of $M_{H,Y}^s(v)$, the moduli space of Gieseker stable sheaves on an Enriques surface $Y$ with Mukai vector $v$ of positive rank with respect to a generic polarization $H$. In the case of a primitive Mukai vector on an unnodal Enriques surface, i.e. one containing no smooth rational curves, we prove irreducibility of $M_{H,Y}(v)$ as well. Using Bayer and Macr`{i}'s construction of a natural nef divisor associated to a stability condition, we explore the relation between wall-crossing in the stability manifold and the minimal model program for Bridgeland moduli spaces. We give three applications of our machinery to obtain new information about the classical moduli spaces of Gieseker-stable sheaves: 1) We obtain a region in the ample cone of the moduli space of Gieseker-stable sheaves over Enriques surfaces. 2) We determine the nef cone of the Hilbert scheme of $n$ points on an unnodal Enriques surface in terms of its half-pencils and the Cossec-Dolgachev $phi$-function. 3) We recover some classical results on linear systems on unnodal Enriques surfaces and obtain some new ones about $n$-very ample line bundles.

ETD_7129

Ph.D.

Includes bibliographical references

by Howard J. Nuer

doi:10.7282/T389181T

ETD doctoral

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