Advanced search options

Advanced Search Options 🞨

Browse by author name (“Author name starts with…”).

Find ETDs with:

in
/  
in
/  
in
/  
in

Written in Published in Earliest date Latest date

Sorted by

Results per page:

Sorted by: relevance · author · university · dateNew search

You searched for +publisher:"University of Illinois – Chicago" +contributor:("Arapura, Donu"). Showing records 1 – 2 of 2 total matches.

Search Limiters

Last 2 Years | English Only

No search limiters apply to these results.

▼ Search Limiters


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.

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

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

2. Pham, Tuan D. On the Picard Varieties of Surfaces with Equivalent Derived Categories.

Degree: 2012, University of Illinois – Chicago

It was shown recently by Popa and Schnell that the irregularities of two smooth projective varieties with equivalent bounded derived categories of coherent sheaves are equal. They conjectured that the Picard varieties of smooth projective varieties with equivalent derived categories are derived equivalent. This thesis investigates this conjecture for the case of smooth projective surfaces. More specifically, we showed that the Picard varieties of derived equivalent surfaces are in fact derived equivalent with the possible exception of the case of properly elliptic surfaces with constant j-invariant. In that case, we also provide an analysis of the Picard variety. In addition, we give a statement about the automorphism groups of derived equivalent surfaces. Advisors/Committee Members: Popa, Mihnea (advisor), Ein, Lawrence (committee member), Coskun, Izzet (committee member), Schnell, Christian (committee member), Arapura, Donu (committee member).

Subjects/Keywords: algebraic geometry; derived categories; Picard varieties; automorphism groups; Albanese varieties; Fourier-Mukai transforms

Page 1 Page 2 Page 3 Page 4 Page 5 Page 6 Page 7

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

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

APA (6th Edition):

Pham, T. D. (2012). On the Picard Varieties of Surfaces with Equivalent Derived Categories. (Thesis). University of Illinois – Chicago. Retrieved from http://hdl.handle.net/10027/9623

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):

Pham, Tuan D. “On the Picard Varieties of Surfaces with Equivalent Derived Categories.” 2012. Thesis, University of Illinois – Chicago. Accessed July 12, 2020. http://hdl.handle.net/10027/9623.

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

MLA Handbook (7th Edition):

Pham, Tuan D. “On the Picard Varieties of Surfaces with Equivalent Derived Categories.” 2012. Web. 12 Jul 2020.

Vancouver:

Pham TD. On the Picard Varieties of Surfaces with Equivalent Derived Categories. [Internet] [Thesis]. University of Illinois – Chicago; 2012. [cited 2020 Jul 12]. Available from: http://hdl.handle.net/10027/9623.

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

Council of Science Editors:

Pham TD. On the Picard Varieties of Surfaces with Equivalent Derived Categories. [Thesis]. University of Illinois – Chicago; 2012. Available from: http://hdl.handle.net/10027/9623

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

.