In algebraic geometry, a Fano variety, introduced by Gino Fano in (Fano 1934, 1942), is an algebraic variety that generalizes certain aspects of complete...

for projective algebraic varieties and complex manifolds. K-stability is of particular importance for the case of Fano varieties, where it is the correct...

elliptic curves, K3 surfaces, and complex Abelian varieties. A complex Fano variety is a complex algebraic variety with ample anti-canonical line bundle (that...

Fano varieties. By definition, a projective variety X is Fano if the anticanonical bundle K X ∗ {\displaystyle K_{X}^{*}} is ample. Fano varieties can...

Fano (Italian: [ˈfaːno]) is a town and comune of the province of Pesaro and Urbino in the Marche region of Italy. It is a beach resort 12 kilometres (7...

Wadden Sea Islands. Fanø Municipality (Danish: Fanø Kommune) is the kommune that covers the island and its seat is the town of Nordby. Fanø is separated from...

geometric invariant theory (GIT) stability. In the special case of Fano varieties, K-stability precisely characterises the existence of Kähler–Einstein...

an algebraic variety Birational geometry Motive (algebraic geometry) Analytic variety Zariski–Riemann space Semi-algebraic set Fano variety Mnëv's universality...

insurgency in the Amhara Region of Ethiopia that began in April 2023 between Fano militia and the Ethiopian government. The conflict began after the Ethiopian...

back to Claude Chevalley. Chow's lemma Theorem of the cube Fano variety Here the product variety X × Y does not carry the product topology, in general; the...

geometry, a Fano fibration or Fano fiber space, named after Gino Fano, is a morphism of varieties whose general fiber is a Fano variety (in other words...

geometry and in global differential geometry, both for bundles and for Fano varieties." In January 2019, he was awarded the Oswald Veblen Prize in Geometry...

decomposition for Calabi–Yau manifolds. By contrast, not every smooth Fano variety has a Kähler–Einstein metric (which would have constant positive Ricci...

{\displaystyle V} is ample, V {\displaystyle V} is called a Fano variety. Suppose that X is a smooth variety and that D is a smooth divisor on X. The adjunction...

minimal models for varieties of log general type". He was awarded the Fields Medal in 2018, "for his proof of boundedness of Fano varieties and contributions...

birational geometry, the minimal model program, and the K-stability of Fano varieties. After completing his PhD doctorate at Princeton under János Kollár's...

Gino Fano (5 January 1871 – 8 November 1952) was an Italian mathematician, best known as the founder of finite geometry. He was born to a wealthy Jewish...

In mathematics, a del Pezzo surface or Fano surface is a two-dimensional Fano variety, in other words a non-singular projective algebraic surface with...

In algebraic geometry, a Fano surface is a surface of general type (in particular, not a Fano variety) whose points index the lines on a non-singular cubic...

Look up Fano or fano in Wiktionary, the free dictionary. Fano is a town in central Italy. Fano may also refer to: Fanø, an island of Denmark Fano, Gijón...

specializing in algebraic geometry, including birational geometry, Fano varieties, and foliations. Araujo was born and raised in Rio de Janeiro, Brazil...

quotient singularities. A weighted projective space is a Q-Fano variety and a toric variety. The weighted projective space P(a0,a1,...,an) is isomorphic...

of degree d ≤ n in Pn is a Fano variety and hence is rationally connected, which is stronger than being uniruled.) A variety X over an uncountable algebraically...

Fano varieties has been achieved by restricting to a special class of K-stable varieties. In this setting important results about boundedness of Fano...

2017. Berman is known for his constributions to the K-stability of Fano varieties. "Robert J. Berman". chalmers.se. Retrieved April 24, 2017. "Robert...

points on suitable algebraic varieties. Their main conjecture is as follows. Let V {\displaystyle V} be a Fano variety defined over a number field K...

Noether–Enriques–Petri theorem, the cone theorem, the existence of a line on smooth Fano varieties and, finally, the existence of log flips—these are several of Shokurov's...

asymptotics of the number of rational points of bounded height on a Fano variety. A variety X over a finite field k has only finitely many k-rational points...

examples of Fano varieties, equivalently, their anticanonical line bundle is ample (in fact very ample). Their index (cf. Fano varieties) is given by...

smooth projective toric varieties, del Pezzo surfaces, many projective homogeneous varieties, and some other Fano varieties. More generally, if X is...