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| 1 | Considering the projective variety of dimension 1 in PG(2, Q) defined by | |
| 2 | x^3 - y^2*z + z^3 | |
| 3 | The same equations, all of the same degree (d = 3) | |
| 4 | x^3 - y^2*z + z^3 | |
| 5 | The dimension vector is (1, 9, 6) | |
| 6 | The 1 morphism(s) defining the variety (i.e. the maps 2->1) are | |
| 7 | x0 - x7 + x9 | |
| 8 | The 3 morphisms defining the d-uple embedding (i.e. the maps 2->3) are described by | |
| 9 | (x0, x1, x2, x3, x4, x5) | |
| 10 | (x1, x3, x4, x6, x7, x8) | |
| 11 | (x2, x4, x5, x7, x8, x9) | |
| 12 | ||
| 13 | Considering the projective variety of dimension 1 in PG(2, Q) defined by | |
| 14 | x^3*y + y^3*z + x*z^3 | |
| 15 | The same equations, all of the same degree (d = 4) | |
| 16 | x^3*y + y^3*z + x*z^3 | |
| 17 | The dimension vector is (1, 14, 10) | |
| 18 | The 1 morphism(s) defining the variety (i.e. the maps 2->1) are | |
| 19 | x1 + x9 + x11 | |
| 20 | The 3 morphisms defining the d-uple embedding (i.e. the maps 2->3) are described by | |
| 21 | (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) | |
| 22 | (x1, x3, x4, x6, x7, x8, x10, x11, x12, x13) | |
| 23 | (x2, x4, x5, x7, x8, x9, x11, x12, x13, x14) | |
| 24 | ||
| 25 | Considering the projective variety of dimension 2 in PG(3, Q) defined by | |
| 26 | x^4 + y^4 + x*y*z*w + z^2*w^2 - w^4 | |
| 27 | The same equations, all of the same degree (d = 4) | |
| 28 | x^4 + y^4 + x*y*z*w + z^2*w^2 - w^4 | |
| 29 | The dimension vector is (1, 34, 20) | |
| 30 | The 1 morphism(s) defining the variety (i.e. the maps 2->1) are | |
| 31 | x0 + x14 + x20 + x32 - x34 | |
| 32 | The 4 morphisms defining the d-uple embedding (i.e. the maps 2->3) are described by | |
| 33 | (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) | |
| 34 | (x1, x4, x5, x6, x10, x11, x12, x13, x14, x15, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29) | |
| 35 | (x2, x5, x7, x8, x11, x13, x14, x16, x17, x18, x21, x23, x24, x26, x27, x28, x30, x31, x32, x33) | |
| 36 | (x3, x6, x8, x9, x12, x14, x15, x17, x18, x19, x22, x24, x25, x27, x28, x29, x31, x32, x33, x34) | |
| 37 | ||
| 38 | - | Considering the projective variety of dimension 1 in PG(3, Q) defined by |
| 38 | + | Considering the projective variety of dimension 2 in PG(4, Q) defined by |
| 39 | - | x0 + x1 + x2 + x3 |
| 39 | + | x0 + x1 + x2 + x3 + x4 |
| 40 | - | x0^3 + x1^3 + x2^3 + x3^3 |
| 40 | + | x0^3 + x1^3 + x2^3 + x3^3 + x4^3 |
| 41 | The same equations, all of the same degree (d = 3) | |
| 42 | - | x0^3 + x0^2*x1 + x0^2*x2 + x0^2*x3 |
| 42 | + | x0^3 + x0^2*x1 + x0^2*x2 + x0^2*x3 + x0^2*x4 |
| 43 | - | x0^3 + x1^3 + x2^3 + x3^3 |
| 43 | + | x0^3 + x1^3 + x2^3 + x3^3 + x4^3 |
| 44 | - | The dimension vector is (1, 19, 10) |
| 44 | + | The dimension vector is (1, 34, 15) |
| 45 | The 2 morphism(s) defining the variety (i.e. the maps 2->1) are | |
| 46 | - | x0 + x1 + x2 + x3 |
| 46 | + | x0 + x1 + x2 + x3 + x4 |
| 47 | - | x0 + x10 + x16 + x19 |
| 47 | + | x0 + x15 + x25 + x31 + x34 |
| 48 | The 5 morphisms defining the d-uple embedding (i.e. the maps 2->3) are described by | |
| 49 | (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) | |
| 50 | - | (x1, x4, x5, x6, x10, x11, x12, x13, x14, x15) |
| 50 | + | (x1, x5, x6, x7, x8, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24) |
| 51 | - | (x2, x5, x7, x8, x11, x13, x14, x16, x17, x18) |
| 51 | + | (x2, x6, x9, x10, x11, x16, x19, x20, x21, x25, x26, x27, x28, x29, x30) |
| 52 | - | (x3, x6, x8, x9, x12, x14, x15, x17, x18, x19) |
| 52 | + | (x3, x7, x10, x12, x13, x17, x20, x22, x23, x26, x28, x29, x31, x32, x33) |
| 53 | (x4, x8, x11, x13, x14, x18, x21, x23, x24, x27, x29, x30, x32, x33, x34) |
