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University of Illinois – Chicago

1. Niu, Wenbo. Bounding the Castelnuovo-Mumford Regularity of Algebraic Varieties.

Degree: 2012, University of Illinois – Chicago

In this monograph, we study bounds for the Castelnuovo-Mumford regularity of algebraic varieties. In chapter three, we give a computational bounds for an homogeneous ideal, which extend a result of Chardin and Ulrich. Our approach is based on liaison theory and a study on singularities in a generic linkage. In chapter four, via Nadel's vanishing theorems and multiplier ideal sheaves, we obtain a vanishing theorem for an ideal sheaf, which extends a result of Bertram, Ein and Lazarsfeld and a result of deFernex and Ein. Our theorem also leads to a regularity bound for powers of ideal sheaves. We also discuss applications of multiplier ideal sheaves in the study of multiregularity on a biprojective space. In Chapter five, we study the asymptotic behavior of the regularity of ideal sheaves, We showed that the asymptotic regularity can be bounded by linear functions, this answers a question raised by Cutkosky and Kurano, and also extends a result of Cutkosky, Ein and Lazarsfeld. We also study asymptotic regularity of symbolic powers and give liner function bounds under some conditions. In Chapter six, we give a sharp regularity bounds for a normal surface with rational, Gorenstein elliptic, log canonical singularities. This result verifies a conjecture of Eisenbud-Goto in normal surfaces case. In Chapter seven, we study a notion of Mukai regularity on abelian varieties. We give a bound for M-regularity of curves in abelian varieties. Our approach is based on vanishing theorems and multiplier ideal sheaves. Advisors/Committee Members: Ein, Lawrence (advisor), Arapura, Donu (committee member), Coskun, Izzet (committee member), Popa, Mihnea (committee member), Schnell, Christian (committee member).

Subjects/Keywords: Castelnuovo-Mumford regularity; powers of ideals; symbolic powers; multiplier ideal sheaves; vanishing theorems; asymptotic regularity; multiregularity; Mukai regularity.

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Niu, W. (2012). Bounding the Castelnuovo-Mumford Regularity of Algebraic Varieties. (Thesis). University of Illinois – Chicago. Retrieved from http://hdl.handle.net/10027/9630

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Niu, Wenbo. “Bounding the Castelnuovo-Mumford Regularity of Algebraic Varieties.” 2012. Thesis, University of Illinois – Chicago. Accessed July 12, 2020. http://hdl.handle.net/10027/9630.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Niu, Wenbo. “Bounding the Castelnuovo-Mumford Regularity of Algebraic Varieties.” 2012. Web. 12 Jul 2020.

Vancouver:

Niu W. Bounding the Castelnuovo-Mumford Regularity of Algebraic Varieties. [Internet] [Thesis]. University of Illinois – Chicago; 2012. [cited 2020 Jul 12]. Available from: http://hdl.handle.net/10027/9630.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Niu W. Bounding the Castelnuovo-Mumford Regularity of Algebraic Varieties. [Thesis]. University of Illinois – Chicago; 2012. Available from: http://hdl.handle.net/10027/9630

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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