The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension...

Grothendieck–Riemann–Roch theorem is a far-reaching result on coherent cohomology. It is a generalisation of the Hirzebruch–Riemann–Roch theorem, about complex...

In mathematics, the Hirzebruch–Riemann–Roch theorem, named after Friedrich Hirzebruch, Bernhard Riemann, and Gustav Roch, is Hirzebruch's 1954 result generalizing...

Soulé is the arithmetic Riemann–Roch theorem of Gillet & Soulé (1992), an extension of the Grothendieck–Riemann–Roch theorem to arithmetic varieties....

In mathematics, the Riemann–Roch theorem for surfaces describes the dimension of linear systems on an algebraic surface. The classical form of it was first...

examples included the Riemann–Roch theorem and its generalization the Hirzebruch–Riemann–Roch theorem, and the Hirzebruch signature theorem. Friedrich Hirzebruch...

compact Riemann surface is a complex algebraic curve by Chow's theorem and the Riemann–Roch theorem. There are several equivalent definitions of a Riemann surface...

are various generalizations of the Riemann–Roch theorem; among the most famous is the Grothendieck–Riemann–Roch theorem, which is further generalized by...

classical Riemann–Roch theorem to higher dimensions, in the Hirzebruch–Riemann–Roch theorem and the Grothendieck–Hirzebruch–Riemann–Roch theorem. It is named...

proved the theorem in full generality connecting global topology with local geometry. The Riemann–Roch theorem and the Atiyah–Singer index theorem are other...

according to the Riemann–Roch theorem and its generalizations, the Hirzebruch–Riemann–Roch theorem and the Grothendieck–Riemann–Roch theorem. For example...

quadratic form. This theorem is proven using the Nakai criterion and the Riemann-Roch theorem for surfaces. The Hodge index theorem is used in Deligne's...

theorem Riemann–Roch theorem for smooth manifolds Riemann–Roch theorem for surfaces Grothendieck–Hirzebruch–Riemann–Roch theorem Hirzebruch–Riemann–Roch...

{\displaystyle \Omega _{X/k}} . The Riemann–Roch theorem and its far-reaching generalization, the Grothendieck–Riemann–Roch theorem, contain as a crucial ingredient...

a Riemann–Roch theorem for smooth manifolds is a version of results such as the Hirzebruch–Riemann–Roch theorem or Grothendieck–Riemann–Roch theorem (GRR)...

the Riemann–Roch theorem to higher dimension is the Hirzebruch–Riemann–Roch theorem, as well as the far-reaching Grothendieck–Riemann–Roch theorem. Hilbert...

Adolph Roch (German: [ʀɔχ]; 9 December 1839 – 21 November 1866) was a German mathematician who made significant contributions to the theory of Riemann surfaces...

properties of a function defined on Riemann surfaces. For example, the Riemann–Roch theorem (Roch was a student of Riemann) says something about the number...

geometry was the Grothendieck–Hirzebruch–Riemann–Roch theorem, a generalisation of the Hirzebruch–Riemann–Roch theorem proved algebraically; in this context...

numbers called the L-genus. It was used in the proof of the Hirzebruch–Riemann–Roch theorem. The L-genus is the genus for the multiplicative sequence of polynomials...

index theorem. Today, the formula is known to follow from the Riemann–Roch formula for quotient stacks. Tetsuro Kawasaki. The Riemann-Roch theorem for complex...

manifold) Arakelyan's theorem (complex analysis) Area theorem (conformal mapping) (complex analysis) Arithmetic Riemann–Roch theorem (algebraic geometry)...

of H0(X, O(mD)) grows linearly in m for m sufficiently large. The Riemann–Roch theorem is a more precise statement along these lines. On the other hand...

Analytic continuation Riemann sphere Riemann surface Riemann mapping theorem Carathéodory's theorem (conformal mapping) Riemann–Roch theorem Amplitwist Antiderivative...

holomorphic Euler characteristic that can be computed using the Hirzebruch–Riemann–Roch theorem. The statement of Kunihiko Kodaira's result is that if M is a compact...

K-theory approach include the Grothendieck–Riemann–Roch theorem, Bott periodicity, the Atiyah–Singer index theorem, and the Adams operations. In high energy...

invertible sheaf or line bundle associated to D. This means that, by the Riemann–Roch theorem, the H0 cohomology or space of holomorphic sections is larger than...

representation Reuleaux triangle Ribaucour curve[3][4] Riemann–Hurwitz formula Riemann–Roch theorem Riemann surface Road curve Sato–Tate conjecture secant Singular...

of the Riemann–Roch theorem (see also Riemann–Roch theorem for algebraic curves) and of the Riemann–Hurwitz formula. By the Riemann-Roch theorem, an irreducible...

examples included the Riemann–Roch theorem and its generalization the Hirzebruch–Riemann–Roch theorem, and the Hirzebruch signature theorem. Hirzebruch and...