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__Sign Up__- Considering the projective variety of dimension 1 in PG(2, Q) defined by
- x^3 - y^2*z + z^3
- The same equations, all of the same degree (d = 3)
- x^3 - y^2*z + z^3
- The dimension vector is (1, 9, 6)
- The 1 morphism(s) defining the variety (i.e. the maps 2->1) are
- x0 - x7 + x9
- The 3 morphisms defining the d-uple embedding (i.e. the maps 2->3) are described by
- (x0, x1, x2, x3, x4, x5)
- (x1, x3, x4, x6, x7, x8)
- (x2, x4, x5, x7, x8, x9)
- Considering the projective variety of dimension 1 in PG(2, Q) defined by
- x^3*y + y^3*z + x*z^3
- The same equations, all of the same degree (d = 4)
- x^3*y + y^3*z + x*z^3
- The dimension vector is (1, 14, 10)
- The 1 morphism(s) defining the variety (i.e. the maps 2->1) are
- x1 + x9 + x11
- The 3 morphisms defining the d-uple embedding (i.e. the maps 2->3) are described by
- (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
- (x1, x3, x4, x6, x7, x8, x10, x11, x12, x13)
- (x2, x4, x5, x7, x8, x9, x11, x12, x13, x14)
- Considering the projective variety of dimension 2 in PG(3, Q) defined by
- x^4 + y^4 + x*y*z*w + z^2*w^2 - w^4
- The same equations, all of the same degree (d = 4)
- x^4 + y^4 + x*y*z*w + z^2*w^2 - w^4
- The dimension vector is (1, 34, 20)
- The 1 morphism(s) defining the variety (i.e. the maps 2->1) are
- x0 + x14 + x20 + x32 - x34
- The 4 morphisms defining the d-uple embedding (i.e. the maps 2->3) are described by
- (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19)
- (x1, x4, x5, x6, x10, x11, x12, x13, x14, x15, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29)
- (x2, x5, x7, x8, x11, x13, x14, x16, x17, x18, x21, x23, x24, x26, x27, x28, x30, x31, x32, x33)
- (x3, x6, x8, x9, x12, x14, x15, x17, x18, x19, x22, x24, x25, x27, x28, x29, x31, x32, x33, x34)
- Considering the projective variety of dimension 2 in PG(4, Q) defined by
- x0 + x1 + x2 + x3 + x4
- x0^3 + x1^3 + x2^3 + x3^3 + x4^3
- The same equations, all of the same degree (d = 3)
- x0^3 + x0^2*x1 + x0^2*x2 + x0^2*x3 + x0^2*x4
- x0^3 + x1^3 + x2^3 + x3^3 + x4^3
- The dimension vector is (1, 34, 15)
- The 2 morphism(s) defining the variety (i.e. the maps 2->1) are
- x0 + x1 + x2 + x3 + x4
- x0 + x15 + x25 + x31 + x34
- The 5 morphisms defining the d-uple embedding (i.e. the maps 2->3) are described by
- (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)
- (x1, x5, x6, x7, x8, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24)
- (x2, x6, x9, x10, x11, x16, x19, x20, x21, x25, x26, x27, x28, x29, x30)
- (x3, x7, x10, x12, x13, x17, x20, x22, x23, x26, x28, x29, x31, x32, x33)
- (x4, x8, x11, x13, x14, x18, x21, x23, x24, x27, x29, x30, x32, x33, x34)

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