Zhang Shuwen hesitated for a moment, then chose to stand up, walked to Qiao Yu's side, casually wiped off the last of the board notes, and began his on-the-spot explanation.
"The Riemann-Roch theorem is a fundamental theorem in Algebraic Geometry used to describe the dimensions of certain functions or forms on algebraic curves. Specifically, the Riemann-Roch theorem applies to any divisor D on an algebraic curve X, and the theorem states the dimension of the function space L(D) associated with the divisor D on the algebraic curve.
Its specific statement is ℓ(D) = deg(D) + 1 − g + ℓ(K−D). It has two parts that complement each other, describing the balance relationship between the divisor D and the remaining part K−D. However, there are special cases, when the degree of D is large enough, then ℓ(K−D) is zero, so in this case, ℓ(D) = deg(D) + 1 − g, do you understand what this means?"
