M(8,5,2) - Revision history

Charles Eaton at 20:49, 5 December 2018

2018-12-05T20:49:29Z

2018-12-05T08:44:52Z

PIgroup and more detail on Pic

2018-12-05T08:28:11Z

2018-11-21T16:15:06Z

@@ Line 30: / Line 30: @@
 |O-morita-frob = 1
 |Pic-O =  <math>C_2 \times C_2</math><ref><math>{\rm Pic}_{\mathcal{O}}(B_0(\mathcal{O}(C_2 \times A_5)))=\mathcal{L}(B_0(\mathcal{O}(C_2 \times A_5)))=\mathcal{L}(\mathcal{O}C_2) \times \mathcal{T}(B_0(\mathcal{O}A_5))</math> by [[References|[EL18c]]], giving the isomorphism type of <math>{\rm Pic}_\mathcal{O}(B)</math> in general.</ref>
-|PIgroup = <math>C_2 \times S_4 \times C_2</math><ref>By Theorem 3.7 of [[References|[EL18c]]].</ref>
+|PIgroup = <math>S_4 \times C_2 \times C_2</math><ref>By Theorem 3.7 of [[References|[EL18c]]].</ref>
 |source? = No
 |sourcereps =

@@ Line 29: / Line 29: @@
 \end{array}\right)</math>
 |O-morita-frob = 1
-|Pic-O =  <math>C_2 \times C_2</math><ref>See [[References|[EL18c]]]</ref>
+|Pic-O =  <math>C_2 \times C_2</math><ref><math>{\rm Pic}_{\mathcal{O}}(B_0(\mathcal{O}(C_2 \times A_5)))=\mathcal{L}(B_0(\mathcal{O}(C_2 \times A_5)))=\mathcal{L}(\mathcal{O}C_2) \times \mathcal{T}(B_0(\mathcal{O}A_5))</math> by [[References|[EL18c]]], giving the isomorphism type of <math>{\rm Pic}_\mathcal{O}(B)</math> in general.</ref>
 |source? = No
-|sourcereps = &nbsp;
+|sourcereps =
 |k-derived-known? = Yes
 |k-derived = [[M(8,5,2)]]

@@ Line 37: / Line 37: @@
 |coveringblocks =
 |coveredblocks =
 }}
@@ Line 45: / Line 46: @@
 '''Quiver:''' a:<1,2>, b:<2,3>, c:<3,2>, d:<2,1>, e:<1,1>, f: <2,2>, g:<3,3>
-'''Relations w.r.t. <math>k</math>:''' ad=cb=0, bcda=dabc, e^2=f^2=g^2=0, af=ea, bg=fb, cf=gc, de=fd
+'''Relations w.r.t. <math>k</math>:''' <math>ad=cb=0</math>, <math>bcda=dabc</math>, <math>e^2=f^2=g^2=0</math>, <math>af=ea</math>, <math>bg=fb</math>, <math>cf=gc</math>, <math>de=fd</math>
 == Other notatable representatives ==