<mods:mods xmlns:mods="http://www.loc.gov/mods/v3" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-4.xsd"><mods:titleInfo><mods:title>Cremona transformations and rational parametrizations inspired by Hodge theory</mods:title></mods:titleInfo><mods:name type="personal"><mods:namePart>Lai, Kuan-Wen</mods:namePart><mods:role><mods:roleTerm type="text">creator</mods:roleTerm></mods:role></mods:name><mods:name type="personal"><mods:namePart>Hassett, Brendan</mods:namePart><mods:role><mods:roleTerm type="text">Advisor</mods:roleTerm></mods:role></mods:name><mods:name type="personal"><mods:namePart>Abramovich, Dan</mods:namePart><mods:role><mods:roleTerm type="text">Reader</mods:roleTerm></mods:role></mods:name><mods:name type="personal"><mods:namePart>Silverman, Joseph</mods:namePart><mods:role><mods:roleTerm type="text">Reader</mods:roleTerm></mods:role></mods:name><mods:name type="corporate"><mods:namePart>Brown University. Department of Mathematics</mods:namePart><mods:role><mods:roleTerm type="text">sponsor</mods:roleTerm></mods:role></mods:name><mods:originInfo><mods:copyrightDate>2018</mods:copyrightDate></mods:originInfo><mods:physicalDescription><mods:extent>viii, 120 p.</mods:extent><mods:digitalOrigin>born digital</mods:digitalOrigin></mods:physicalDescription><mods:note type="thesis">Thesis (Ph. D.)--Brown University, 2018</mods:note><mods:genre authority="aat">theses</mods:genre><mods:abstract>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 a birational automorphism of projective fourfold with base loci birational to nontrivially derived equivalent K3 surfaces. The second is about the rationality problem of cubic fourfolds. We present two examples of cubic fourfolds which contain families of rational scrolls naturally arise from their Hodge structures. By exploiting the rational scrolls, we show that one example is rational and the other one admits unirational parametrizations of odd degree.</mods:abstract><mods:subject authority="fast" authorityURI="http://id.worldcat.org/fast" valueURI="http://id.worldcat.org/fast/00940902"><mods:topic>Geometry, Algebraic</mods:topic></mods:subject><mods:language><mods:languageTerm authority="iso639-2b">English</mods:languageTerm></mods:language><mods:recordInfo><mods:recordContentSource authority="marcorg">RPB</mods:recordContentSource><mods:recordCreationDate encoding="iso8601">20180615</mods:recordCreationDate></mods:recordInfo><mods:identifier type="doi">10.26300/yv4t-6v86</mods:identifier><mods:accessCondition type="rights statement" xlink:href="http://rightsstatements.org/vocab/InC/1.0/">In Copyright</mods:accessCondition><mods:accessCondition type="restriction on access">Collection is open for research.</mods:accessCondition><mods:typeOfResource authority="primo">dissertations</mods:typeOfResource></mods:mods>