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Hyperplane Arrangements

Thesis Info

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Author

Nazir, Shaheen

Supervisor

Alexandru Dimca

Program

PhD

Institute

Government College University

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2007

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/1951

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726384529

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Let A = {H 1 , . . . , H l } be a hyperplane arrangement in C n and M be the complement of the union of hyperplanes in A, i.e., M = C n \ ∪ li=1 H i . The cohomology algebra H ∗ (M, C) has a complete combinatorial description. Let L be a local system on M and H ∗ (M, L) be the cohomology algebra with local coefficients. For [ω] ∈ H 1 (M, C), there is a chain complex: μ ω μ ω μ ω 0 → H 0 (M, C) → H 1 (M, C) → · · · → H n (M, C) → 0. The characteristic varieties of M are the jumping loci of the cohomology groups H ∗ (M, L). The resonance varieties of M are the jumping loci of the cohomology groups of the above complex. The aim of this thesis is to study some properties of these varieties.
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عشق آمادہ ہیں گل دیکھ کے صورت اس کی

عشق آمادہ ہیں گل دیکھ کے صورت اس کی
جی جلاتی ہے گھڑی بھر میں محبت اس کی

اس ستم گر کی نگاہوں کا سحر، اُف توبہ
جان دی جس نے، کہو خوب ہے قسمت اس کی

صبح کا نور ہو یا پھر ہو شفق کی سرخی
نور و نکہت سے بیاں کیسے ہو رنگت اس کی

وصل اور ہجر محبت کے پیمبر ہیں مگر
شب کی آغوش سے ملتی ہے طبیعت اس کی

اس کی آواز لپکتا ہوا شعلہ ہے فضاؔ
مجھ کو آواز بھی لگتی ہے قیامت اس کی

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