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Browsing Mathematics by Author "Robles, Colleen"
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- Completion 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 bundle360 113 - Completions 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?334 175 - Completions 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.418 297 - Global 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 surfaces324 132 - Global 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 References300 159 - Moduli 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.234 136 - Natural 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.276 190 - New 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.236 106 - Period Mapping and the properties of the Hodge line bundle(2020-07)
;Griffiths, Phillip ;Green, Mark ;Laza, RaduRobles, Colleen340 257 - Towards 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.313 188