Аналитическая геометрия. Часть III. Многомерные пространства. Гиперповерхности второго порядка. Шурыгин В.В. - 78 стр.

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P
n
m (m ) P
n
π
m
⊂ P
n
π
m
= p(V
m+1
\ {0})
V
m+1
= V
m+1
(π
m
) V
n+1
P
n
p V
m+1
\ {0}
π
m
⊂ P
n
m P
m
P
n
P
n
π
m
= p(V
m+1
\
{0})
π(V
m+1
)
0
O
P
n
V
m+1
P
m
= π
m
P
n
1 P
n
(n − 1)
π(V
m+1
) π(V
0
k+1
) P
n
V
m+1
∩ V
0
k+1
6=
{0}
π(V
m+1
) ∩ π(V
0
k+1
) = π(V
m+1
∩ V
0
k+1
).
V
m+1
∩ V
0
k+1
= {0} π(V
m+1
) π(V
0
k+1
)
P
n
π
m
π
k
P
n
(m + 1) + (k + 1) 6 n + 1 ⇔ m + k 6 n − 1
O
M
a
b
V
1
(M)
V
2
(a)
V
2
(b)
2 P
2
a b
M = a ∩ b
1
V
1
(M) = V
2
(a) ∩ V
2
(b).
P
2
= S
2
/∼
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kjmiht egndbgymhikg πm ⊂ Pn ijvgmw sig πm = p(Vm+1 \ {0}) w xnm
                                                               n

                       n                   v
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jhhg†aafgkjbbgd h Pn €
   )*B0D,-  -7-+35“*,0* p  -935,0)*,,-* ,5 V \ {0}  ,5D*68*7 .-D
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                                               m+1


’-¨7-:2 .6-/1-/70 B Pn ,5EAB5‡7 751“* egnefghifjbhikjda B Pn < 68
-+-E,5)*,08 .6-/1-/70 πm = p(Vm+1 \
{0}) +2D*: 0/.-6>E-B57> 751“* -+-E,5
)*,0* π(V ) <                                      Pm = πm

   0 .6-/1-/70 B .3-*170B,-: .3-/735,
             m+1
                                                                   Pn
/7B* Pn F ¨7- 7-)10 ¨7-9- .3-/735,/7B5<
1 .6-/1-/70 .3-/735,/7B5 Pn ,5EAB5‡7                      Vm+1
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          v
emfeogh ghitda<
   ’2/7> π(Vm+1) 0 π(Vk+1
                        0                          
                           ) F DB* .6-/1-/70 B Pn < /60 Vm+1 ∩ Vk+1
                                                                 0
                                                                      6=
            )
{0}  7-  - *B0D,- 
                                0                 0
                  π(Vm+1 ) ∩ π(Vk+1 ) = π(Vm+1 ∩ Vk+1 ).
/60 V ∩ V0 = {0}  7- .6-/1-/70 π(V ) 0 π(V0 ) ,5EAB5‡7/8
hvfmqakj{qadaht        510: -+35E-:   DB* .6-/1-/70  B    60+-  .*3*/*15‡7/8
        m+1      k+1                           m+1          k+1
                     <                                Pn
.- .6-/1-/70 60+- /13*ˆ0B5‡7/8 < ’6-/1-/70 πm 0 πk B Pn :-927 /13*ˆ0
B57>/8 7-6>1- .30 (m + 1) + (k + 1) 6 n + 1 ⇔ m + k 6 n − 1 <
      )5/7,-/70  ,5 .3-*170B,-” .6-/1-
/70 •751 ,5EAB5‡7 .3-*170B,-* .3-/735,                     M       b
/7B- 35E:*3,-/70 2‹ P2 6‡+A* DB* ,*/-B                        a
.5D5‡ˆ0* .38:A* a 0 b .*3*/*15‡7/8 B
-D,-” 7-)1* < ³75 7-)15 M = a ∩ b -.3*        V2 (b)
D*68*7/8 1 :*3,A: .-D.3-/735,/7B-:                         O         V2 (a)
                                               V1 (M )
        V1 (M ) = V2 (a) ∩ V2 (b).
  :-D*60 P2 = S2/∼ ¨7- /B-”/7B- .38:AC .3-*170B,-” .6-/1-/70 066‡
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