The number of conjugacy classes of elements of the Cremona group
... We are now able to prove Theorem 1.2, i.e. to show the existence of infinitely many conjugacy classes of elements of order n in the Cremona group, for any even integer n and for n = 3, 5. Proof of Theorem 1.2. — First of all, taking some non-rational curve Γ, any birational transformation sends Γ on ...
... We are now able to prove Theorem 1.2, i.e. to show the existence of infinitely many conjugacy classes of elements of order n in the Cremona group, for any even integer n and for n = 3, 5. Proof of Theorem 1.2. — First of all, taking some non-rational curve Γ, any birational transformation sends Γ on ...
Trigonometric Identities and Sums of Separable Functions
... Because of Lemma 1 and Theorem 2, we know that sin( j=1 xj ) is exactly separated with separation rank n. Moreover, this function is peculiar in that sin(·) is the only function used in the separated representation. We now consider the problem of finding other functions s(x) satisfying (6). Since th ...
... Because of Lemma 1 and Theorem 2, we know that sin( j=1 xj ) is exactly separated with separation rank n. Moreover, this function is peculiar in that sin(·) is the only function used in the separated representation. We now consider the problem of finding other functions s(x) satisfying (6). Since th ...
ON SEQUENTIALLY COHEN-MACAULAY
... A poset P is said to be pure, sequentially connected, sequentially acyclic, SCM, or SHCM if its order complex ∆(P ) is, where ∆(P ) is the simplicial complex of chains of P . The paper is organized as follows. In Section 2, we show that a SHCM complex has the homotopy type of a wedge of spheres in t ...
... A poset P is said to be pure, sequentially connected, sequentially acyclic, SCM, or SHCM if its order complex ∆(P ) is, where ∆(P ) is the simplicial complex of chains of P . The paper is organized as follows. In Section 2, we show that a SHCM complex has the homotopy type of a wedge of spheres in t ...
