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The number of coincidences of a (nu,nu^') correspondence of value gamma on a curve of curve genus p is given by nu+nu^'+2pgamma.

If a one-parameter family of curves has index N and class M, the number tangent to a curve of order n_1 and class m_1 in general position is m_1N+n_1M.

The intersection product for classes of rational equivalence between cycles on an algebraic variety.

The set C_(n,m,d) of all m-D varieties of degree d in an n-dimensional projective space P^n into an M-D projective space P^M.

sum_(k=0)^m(phi_k(x)phi_k(y))/(gamma_k)=(phi_(m+1)(x)phi_m(y)-phi_m(x)phi_(m+1)(y))/(a_mgamma_m(x-y),) (1) where phi_k(x) are orthogonal polynomials with weighting function ...

Let {p_n(x)} be orthogonal polynomials associated with the distribution dalpha(x) on the interval [a,b]. Also let rho=c(x-x_1)(x-x_2)...(x-x_l) (for c!=0) be a polynomial of ...

Chrystal's identity is the algebraic identity ((b-c)^2+(b+c)^2+2(b^2-c^2))/((b^4-2b^2c^2+c^4)[1/((b-c)^2)+2/(b^2-c^2)+1/((b+c)^2)])=1 given as an exercise by Chrystal (1886).

A class number formula is a finite series giving exactly the class number of a ring. For a ring of quadratic integers, the class number is denoted h(d), where d is the ...

Classical algebraic geometry is the study of algebraic varieties, both affine varieties in C^n and projective algebraic varieties in CP^n. The original motivation was to ...

The four following types of groups, 1. linear groups, 2. orthogonal groups, 3. symplectic groups, and 4. unitary groups, which were studied before more exotic types of groups ...