SlideShare una empresa de Scribd logo
1 de 2
a = 6, b = 2 are the values
Let
a
xyz -
a
y^3
+xz^2 =
bw^3
be a homogenous polynomial in
P3
(
x,y,z,w
), describing an algebraic variety V in
P3
.
1. Show the view of V in affine patches
Ux, Uy, Uz, Uw.
when x=1,y=1, z=1, w=1.
2. What is the dimension of V?
3. Is V an irreducible variety?
4. Find all singular points.
5. Give the ideal of
V
. Is it prime? Is your variety irreducible? Describe the ring k(
V
) = O(V) of polynomials (regular functions) on
V
.
6. Calculate curvature at (at least two) smooth points.
Curvature_surfaces _definition.docx
Actions
7. Describe the symmetries of your surface
V. Is it
bounded or unbounded?
8. Can you find a line on your surface?

Más contenido relacionado

Más de taishao1

8B20M017 Teaching Note SOBEYS—PROJECT SUNRIS.docx
8B20M017  Teaching Note  SOBEYS—PROJECT SUNRIS.docx8B20M017  Teaching Note  SOBEYS—PROJECT SUNRIS.docx
8B20M017 Teaching Note SOBEYS—PROJECT SUNRIS.docx
taishao1
 
81Journal of International Studies© Foundation .docx
81Journal of International Studies© Foundation .docx81Journal of International Studies© Foundation .docx
81Journal of International Studies© Foundation .docx
taishao1
 
82916 f_ch02.docx 45 Chapter 2 From Public Regulat.docx
82916 f_ch02.docx  45 Chapter 2 From Public Regulat.docx82916 f_ch02.docx  45 Chapter 2 From Public Regulat.docx
82916 f_ch02.docx 45 Chapter 2 From Public Regulat.docx
taishao1
 
8. On the likely aftermath and long term effects of the coronavi.docx
8. On the likely aftermath and long term effects of the coronavi.docx8. On the likely aftermath and long term effects of the coronavi.docx
8. On the likely aftermath and long term effects of the coronavi.docx
taishao1
 
776! CHAPTER 26 Rococo to Neoclassicism The 18th Century in E.docx
776! CHAPTER 26 Rococo to Neoclassicism The 18th Century in E.docx776! CHAPTER 26 Rococo to Neoclassicism The 18th Century in E.docx
776! CHAPTER 26 Rococo to Neoclassicism The 18th Century in E.docx
taishao1
 
8 New Scientist 4 January 2020THE tropics are the most.docx
8  New Scientist  4 January 2020THE tropics are the most.docx8  New Scientist  4 January 2020THE tropics are the most.docx
8 New Scientist 4 January 2020THE tropics are the most.docx
taishao1
 
7 HYPOTHETICALS AND YOU TESTING YOUR QUESTIONS7 MEDIA LIBRARY.docx
7 HYPOTHETICALS AND YOU TESTING YOUR QUESTIONS7 MEDIA LIBRARY.docx7 HYPOTHETICALS AND YOU TESTING YOUR QUESTIONS7 MEDIA LIBRARY.docx
7 HYPOTHETICALS AND YOU TESTING YOUR QUESTIONS7 MEDIA LIBRARY.docx
taishao1
 
78 CONTRADICTIONS The development of the cotton expo.docx
78  CONTRADICTIONS The development of the cotton expo.docx78  CONTRADICTIONS The development of the cotton expo.docx
78 CONTRADICTIONS The development of the cotton expo.docx
taishao1
 
68 En glish Journal 103.4 (2014) 68– 75wanted to write a.docx
68 En glish Journal  103.4 (2014) 68– 75wanted to write a.docx68 En glish Journal  103.4 (2014) 68– 75wanted to write a.docx
68 En glish Journal 103.4 (2014) 68– 75wanted to write a.docx
taishao1
 
7-27Security Guide One-Stop ShoppingCopyright ©.docx
7-27Security Guide One-Stop ShoppingCopyright ©.docx7-27Security Guide One-Stop ShoppingCopyright ©.docx
7-27Security Guide One-Stop ShoppingCopyright ©.docx
taishao1
 

Más de taishao1 (20)

8B20M017 Teaching Note SOBEYS—PROJECT SUNRIS.docx
8B20M017  Teaching Note  SOBEYS—PROJECT SUNRIS.docx8B20M017  Teaching Note  SOBEYS—PROJECT SUNRIS.docx
8B20M017 Teaching Note SOBEYS—PROJECT SUNRIS.docx
 
875 words Include citations for all unoriginal ideas, .docx
875 words Include citations for all unoriginal ideas, .docx875 words Include citations for all unoriginal ideas, .docx
875 words Include citations for all unoriginal ideas, .docx
 
81Journal of International Studies© Foundation .docx
81Journal of International Studies© Foundation .docx81Journal of International Studies© Foundation .docx
81Journal of International Studies© Foundation .docx
 
82916 f_ch02.docx 45 Chapter 2 From Public Regulat.docx
82916 f_ch02.docx  45 Chapter 2 From Public Regulat.docx82916 f_ch02.docx  45 Chapter 2 From Public Regulat.docx
82916 f_ch02.docx 45 Chapter 2 From Public Regulat.docx
 
8.1 What is the difference between RFC 5321 and RFC 53228.docx
8.1 What is the difference between RFC 5321 and RFC 53228.docx8.1 What is the difference between RFC 5321 and RFC 53228.docx
8.1 What is the difference between RFC 5321 and RFC 53228.docx
 
8. On the likely aftermath and long term effects of the coronavi.docx
8. On the likely aftermath and long term effects of the coronavi.docx8. On the likely aftermath and long term effects of the coronavi.docx
8. On the likely aftermath and long term effects of the coronavi.docx
 
8 pagesSelect an agency of the US government and a specific pu.docx
8 pagesSelect an agency of the US government and a specific pu.docx8 pagesSelect an agency of the US government and a specific pu.docx
8 pagesSelect an agency of the US government and a specific pu.docx
 
8 pages Select an agency of the US government and a specific p.docx
8 pages Select an agency of the US government and a specific p.docx8 pages Select an agency of the US government and a specific p.docx
8 pages Select an agency of the US government and a specific p.docx
 
8-1 Discussion Immigration LawsIt is a violation of the immigra.docx
8-1 Discussion Immigration LawsIt is a violation of the immigra.docx8-1 Discussion Immigration LawsIt is a violation of the immigra.docx
8-1 Discussion Immigration LawsIt is a violation of the immigra.docx
 
776! CHAPTER 26 Rococo to Neoclassicism The 18th Century in E.docx
776! CHAPTER 26 Rococo to Neoclassicism The 18th Century in E.docx776! CHAPTER 26 Rococo to Neoclassicism The 18th Century in E.docx
776! CHAPTER 26 Rococo to Neoclassicism The 18th Century in E.docx
 
8 New Scientist 4 January 2020THE tropics are the most.docx
8  New Scientist  4 January 2020THE tropics are the most.docx8  New Scientist  4 January 2020THE tropics are the most.docx
8 New Scientist 4 January 2020THE tropics are the most.docx
 
7 HYPOTHETICALS AND YOU TESTING YOUR QUESTIONS7 MEDIA LIBRARY.docx
7 HYPOTHETICALS AND YOU TESTING YOUR QUESTIONS7 MEDIA LIBRARY.docx7 HYPOTHETICALS AND YOU TESTING YOUR QUESTIONS7 MEDIA LIBRARY.docx
7 HYPOTHETICALS AND YOU TESTING YOUR QUESTIONS7 MEDIA LIBRARY.docx
 
78 CONTRADICTIONS The development of the cotton expo.docx
78  CONTRADICTIONS The development of the cotton expo.docx78  CONTRADICTIONS The development of the cotton expo.docx
78 CONTRADICTIONS The development of the cotton expo.docx
 
68 En glish Journal 103.4 (2014) 68– 75wanted to write a.docx
68 En glish Journal  103.4 (2014) 68– 75wanted to write a.docx68 En glish Journal  103.4 (2014) 68– 75wanted to write a.docx
68 En glish Journal 103.4 (2014) 68– 75wanted to write a.docx
 
7.1 What is the basic building block of an 802.11 WLAN7.2 Def.docx
7.1 What is the basic building block of an 802.11 WLAN7.2 Def.docx7.1 What is the basic building block of an 802.11 WLAN7.2 Def.docx
7.1 What is the basic building block of an 802.11 WLAN7.2 Def.docx
 
7-1 Discussion Discovery and Judicial EfficiencyAfter reviewing.docx
7-1 Discussion Discovery and Judicial EfficiencyAfter reviewing.docx7-1 Discussion Discovery and Judicial EfficiencyAfter reviewing.docx
7-1 Discussion Discovery and Judicial EfficiencyAfter reviewing.docx
 
7.4 - Discussion Aircraft SystemsIn this video, Professor S.docx
7.4 - Discussion Aircraft SystemsIn this video, Professor S.docx7.4 - Discussion Aircraft SystemsIn this video, Professor S.docx
7.4 - Discussion Aircraft SystemsIn this video, Professor S.docx
 
7-27Security Guide One-Stop ShoppingCopyright ©.docx
7-27Security Guide One-Stop ShoppingCopyright ©.docx7-27Security Guide One-Stop ShoppingCopyright ©.docx
7-27Security Guide One-Stop ShoppingCopyright ©.docx
 
7.  According to scientists; our personality is set by the time we.docx
7.  According to scientists; our personality is set by the time we.docx7.  According to scientists; our personality is set by the time we.docx
7.  According to scientists; our personality is set by the time we.docx
 
7.1 What is the basic building block of an 802.11 WLAN7.2.docx
7.1 What is the basic building block of an 802.11 WLAN7.2.docx7.1 What is the basic building block of an 802.11 WLAN7.2.docx
7.1 What is the basic building block of an 802.11 WLAN7.2.docx
 

Último

The basics of sentences session 3pptx.pptx
The basics of sentences session 3pptx.pptxThe basics of sentences session 3pptx.pptx
The basics of sentences session 3pptx.pptx
heathfieldcps1
 

Último (20)

UGC NET Paper 1 Mathematical Reasoning & Aptitude.pdf
UGC NET Paper 1 Mathematical Reasoning & Aptitude.pdfUGC NET Paper 1 Mathematical Reasoning & Aptitude.pdf
UGC NET Paper 1 Mathematical Reasoning & Aptitude.pdf
 
Jamworks pilot and AI at Jisc (20/03/2024)
Jamworks pilot and AI at Jisc (20/03/2024)Jamworks pilot and AI at Jisc (20/03/2024)
Jamworks pilot and AI at Jisc (20/03/2024)
 
Interdisciplinary_Insights_Data_Collection_Methods.pptx
Interdisciplinary_Insights_Data_Collection_Methods.pptxInterdisciplinary_Insights_Data_Collection_Methods.pptx
Interdisciplinary_Insights_Data_Collection_Methods.pptx
 
Plant propagation: Sexual and Asexual propapagation.pptx
Plant propagation: Sexual and Asexual propapagation.pptxPlant propagation: Sexual and Asexual propapagation.pptx
Plant propagation: Sexual and Asexual propapagation.pptx
 
Kodo Millet PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...
Kodo Millet  PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...Kodo Millet  PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...
Kodo Millet PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...
 
Google Gemini An AI Revolution in Education.pptx
Google Gemini An AI Revolution in Education.pptxGoogle Gemini An AI Revolution in Education.pptx
Google Gemini An AI Revolution in Education.pptx
 
Holdier Curriculum Vitae (April 2024).pdf
Holdier Curriculum Vitae (April 2024).pdfHoldier Curriculum Vitae (April 2024).pdf
Holdier Curriculum Vitae (April 2024).pdf
 
ICT Role in 21st Century Education & its Challenges.pptx
ICT Role in 21st Century Education & its Challenges.pptxICT Role in 21st Century Education & its Challenges.pptx
ICT Role in 21st Century Education & its Challenges.pptx
 
Basic Civil Engineering first year Notes- Chapter 4 Building.pptx
Basic Civil Engineering first year Notes- Chapter 4 Building.pptxBasic Civil Engineering first year Notes- Chapter 4 Building.pptx
Basic Civil Engineering first year Notes- Chapter 4 Building.pptx
 
TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...
TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...
TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...
 
How to Manage Global Discount in Odoo 17 POS
How to Manage Global Discount in Odoo 17 POSHow to Manage Global Discount in Odoo 17 POS
How to Manage Global Discount in Odoo 17 POS
 
Towards a code of practice for AI in AT.pptx
Towards a code of practice for AI in AT.pptxTowards a code of practice for AI in AT.pptx
Towards a code of practice for AI in AT.pptx
 
Accessible Digital Futures project (20/03/2024)
Accessible Digital Futures project (20/03/2024)Accessible Digital Futures project (20/03/2024)
Accessible Digital Futures project (20/03/2024)
 
How to Create and Manage Wizard in Odoo 17
How to Create and Manage Wizard in Odoo 17How to Create and Manage Wizard in Odoo 17
How to Create and Manage Wizard in Odoo 17
 
HMCS Vancouver Pre-Deployment Brief - May 2024 (Web Version).pptx
HMCS Vancouver Pre-Deployment Brief - May 2024 (Web Version).pptxHMCS Vancouver Pre-Deployment Brief - May 2024 (Web Version).pptx
HMCS Vancouver Pre-Deployment Brief - May 2024 (Web Version).pptx
 
The basics of sentences session 3pptx.pptx
The basics of sentences session 3pptx.pptxThe basics of sentences session 3pptx.pptx
The basics of sentences session 3pptx.pptx
 
FSB Advising Checklist - Orientation 2024
FSB Advising Checklist - Orientation 2024FSB Advising Checklist - Orientation 2024
FSB Advising Checklist - Orientation 2024
 
On National Teacher Day, meet the 2024-25 Kenan Fellows
On National Teacher Day, meet the 2024-25 Kenan FellowsOn National Teacher Day, meet the 2024-25 Kenan Fellows
On National Teacher Day, meet the 2024-25 Kenan Fellows
 
Application orientated numerical on hev.ppt
Application orientated numerical on hev.pptApplication orientated numerical on hev.ppt
Application orientated numerical on hev.ppt
 
NO1 Top Black Magic Specialist In Lahore Black magic In Pakistan Kala Ilam Ex...
NO1 Top Black Magic Specialist In Lahore Black magic In Pakistan Kala Ilam Ex...NO1 Top Black Magic Specialist In Lahore Black magic In Pakistan Kala Ilam Ex...
NO1 Top Black Magic Specialist In Lahore Black magic In Pakistan Kala Ilam Ex...
 

a = 6, b = 2 are the valuesLet axyz - ay^3+xz^2  =.docx

  • 1. a = 6, b = 2 are the values Let a xyz - a y^3 +xz^2 = bw^3 be a homogenous polynomial in P3 ( x,y,z,w ), describing an algebraic variety V in P3 . 1. Show the view of V in affine patches Ux, Uy, Uz, Uw. when x=1,y=1, z=1, w=1. 2. What is the dimension of V? 3. Is V an irreducible variety? 4. Find all singular points. 5. Give the ideal of V . Is it prime? Is your variety irreducible? Describe the ring k( V ) = O(V) of polynomials (regular functions) on V .
  • 2. 6. Calculate curvature at (at least two) smooth points. Curvature_surfaces _definition.docx Actions 7. Describe the symmetries of your surface V. Is it bounded or unbounded? 8. Can you find a line on your surface?