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061023 1 Considere Sxyzw 2x2 y2 2z2 w2 0 algebraic variety in R4 Then 0000 is an singular point 2 Considere 5xyz x3 y3 3xz2 3yz2 0 is a singular point 3 Sxy xy 0 Tangent cone in 00 is xy xy 0 4 Considere X cartesian product of two algebraic curves in R2 example xy 0 TCarbon cone in 00 is xyxy 0 x xy xy0 subset R4 In the next page we calculate the TCarbon cone at 0000 by intersection with dim 3 061023 1 Rx Rx Ry 0 µo xo 0 0 µo0 2 Ry µo 3 y2 0 µo0 3 µo 0 NX 00 N2 2 4 Nik Nowadays XRP 2 y 0 NX 0 y 0 Az0 ry 0 At 0 NX4 0 12 At 1 1 2 12 12 2 2 0 2 20 2 1 4 4 1 1 1 1 Area Fuxv 11 2x2 11 2 Tan Dxdy FW 00 z y duw 2 w 20 0 duw 2 20 10 1 10 2 m2 m2 m 2 1 21 1 2x2 20m 0 11