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Browsing Mathematics by Author "Robles, Colleen"
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- Some of the metrics are blocked by yourconsent settingsCompletion of the period mappings and ampleness of the Hodge bundles(2020)
;Griffiths, Phillip ;Green, Mark ;Laza, RaduRobles, ColleenI. Introduction II. Construction of a completion of the image of a period mapping III. Curvature properties of the extended Hodge line bundle (A) IV. Curvature properties of the extended Hodge line bundle (B) V. Proof that the extended Hodge line bundle is ample VI. Curvature properties of the Hodge vector bundle363 166 - Some of the metrics are blocked by yourconsent settingsCompletions of Period Mappings(2020-10-13)
;Griffiths, Phillip ;Green, MarkRobles, ColleenThis work initiates a global study of period mappings at infinity, that is motivated by challenges arising when considering the questions: (i) What are natural completions of a period mapping? (ii) What geometric applications do they have?335 199 - Some of the metrics are blocked by yourconsent settingsCompletions of Period Mappings: Progress Report(2021)
;Griffiths, Phillip ;Green, MarkRobles, ColleenWe give an informal, expository account of a project to construct completions of period maps.420 360 - Some of the metrics are blocked by yourconsent settingsGlobal properties of period mappings on the boundary(2020)
;Griffiths, Phillip ;Green, MarkRobles, ColleenOutline I. Introduction II. Extension data for a mixed Hodge structure III. Extension data for limiting mixed Hodge structures IV. Period mappings to extension data (A) V. Period mappings to extension data (B) Appendix to Sections IV and V: Examples VI. Local Torelli conditions VII. Global structure of period mappings from complete surfaces325 150 - Some of the metrics are blocked by yourconsent settingsGlobal properties of period mappings on the boundary
;Griffiths, Phillip ;Green, MarkRobles, ColleenI. Introduction II. Extension data for a mixed Hodge structure III. Extension data for limiting mixed Hodge structures IV. Period mappings to extension data (A) V. Period mappings to extension data (B) Appendix to Sections IV and V: Examples VI. Local Torelli conditions VII. Global structure of period mappings from complete surfaces VIII. Period mappings and the canonical bundle References301 186 - Some of the metrics are blocked by yourconsent settingsModuli and Hodge Theory(2018-11-12)
;Griffiths, Phillip ;Green, Mark ;Laza, RaduRobles, ColleenTalk at the "Geometry at the Frontier" conference, Pucón, Chile (November 12, 2018), and based in part on joint work in progress with Mark Green, Radu Laza and Colleen Robles.237 225 - Some of the metrics are blocked by yourconsent settingsNatural line bundles on completions of period mappings(2021-02-11)
;Griffiths, Phillip ;Green, MarkRobles, ColleenWe give conditions under which natural lines bundles associated with completions of period mappings are semi-ample and ample.276 211 - Some of the metrics are blocked by yourconsent settingsNew Geometric Invariants Arising from Hodge Theory(2018-12)
;Griffiths, Phillip ;Green, Mark ;Laza, RaduRobles, ColleenThe use of the Hodge line bundle, especially its positivity properties, in algebraic geometry is classical. The Hodge line bundle only sees the associated graded to the limiting mixed Hodge structures (LMHS's) that arise from the singular members in a family of algebraic varieties. This talk will introduce a new type of geometric object associated to the extension data in LMHS's (and not present for general MHS's) whose positivity properties play a central role in the application of Hodge theory to moduli. Their construction will be discussed and illustrated.239 135 - Some of the metrics are blocked by yourconsent settingsPeriod Mapping and the properties of the Hodge line bundle(2020-07)
;Griffiths, Phillip ;Green, Mark ;Laza, RaduRobles, Colleen343 299 - Some of the metrics are blocked by yourconsent settingsTowards a maximal completion of a period map(2021-02-11)
;Griffiths, Phillip ;Green, MarkRobles, ColleenThe motivation behind this work is to construct a "Hodge theoretically maximal" completion of a period map. This is done up to finite data (we work with the Stein factorization of the period map). The image of the extension is a Moishezon variety that compactifies a finite cover of the image of the period map.319 219