Results 201 to 210 of about 2,997,696 (239)

SINGULAR TORIC FANO VARIETIES

Russian Academy of Sciences. Sbornik Mathematics, 1993
The aim of this paper is to justify that there are a finite number of types of singular toroidal varieties satisfying some restrictions concerning their singularities.
Borisov, A. A., Borisov, L. A.
openaire   +1 more source

Mukai bundles on Fano threefolds

Compositio Mathematica
We give a proof of Mukai’s theorem on the existence of certain exceptional vector bundles on prime Fano threefolds. To our knowledge this is the first complete proof in the literature.
Arend Bayer, A. Kuznetsov, Emanuele Macrì   +2 more
semanticscholar   +1 more source

Factorization of Anticanonical Maps of Fano Type Variety

, 2014
The purpose of the present paper is to generalize Sakai's work on anticanonical models of rational surfaces to varieties of Fano type. We rst prove a characterization of Fano type varieties using the singularities of anti- canonical models.
S. Choi, DongSeon Hwang, Jinhyung Park
semanticscholar   +1 more source

G-uniform stability and Kähler–Einstein metrics on Fano varieties

Inventiones Mathematicae, 2019
Let X be any $${{\mathbb {Q}}}$$ Q -Fano variety and $$\mathrm{Aut}(X)_0$$ Aut ( X ) 0 be the identity component of the automorphism group of X . Let $${\mathbb {G}}$$ G be a connected reductive subgroup of $$\mathrm{Aut}(X)_0$$ Aut ( X ) 0 that contains
Chi Li
semanticscholar   +1 more source

Frequency‐Space Selective Fano Resonance Based on a Micro‐Ring Resonator on Lithium Niobate on Insulator

Laser & Photonics Reviews
Corresponding to the different phase‐shifts of the interference modes, the whispering gallery mode resonator‐based Fano resonance exhibits a variety of unique spectral lineshapes that can be applied to sensing, optical signal processing, and so on ...
Tingge Yuan, Xueyi Wang, Jiangwei Wu, Hao Li, Yuping Chen, Xianfeng Chen   +5 more
semanticscholar   +1 more source

ON FANO VARIETIES OF GENUS 6

Mathematics of the USSR-Izvestiya, 1983
Let V be a Fano variety, \(K_ V\) the canonical class of V and \(g=(-K^ s_ V)+1\) the genus of V. Then the anticanonical linear system \(| - K_ V|\) defines a closed immersion \(\phi_{| -K_ V|}:V\overset \sim \rightarrow V_{2g-2}\hookrightarrow {\mathbb{P}}^{g+1}\) where \(V_{2g-2}\) is a projective variety of degree 2g-2.
openaire   +1 more source

Kawamata–Miyaoka type inequality for ℚ-Fano varieties with canonical singularities

Journal für die Reine und Angewandte Mathematik
Let X be an n-dimensional normal ℚ {\mathbb{Q}} -factorial projective variety with canonical singularities and Picard number one such that X is smooth in codimension two, - K X {-K_{X}} is ample and n ≥ 2 {n\geq 2} .
Haidong Liu, Jie Liu
semanticscholar   +1 more source

The Uniform Version of Yau–Tian–Donaldson Conjecture for Singular Fano Varieties

Peking Mathematical Journal, 2019
We prove the following result: if a $$\,\,\,\,\,{\mathbb {Q}}\,\,\,\,\,$$ Q -Fano variety is uniformly K-stable, then it admits a Kähler–Einstein metric.
Chi Li, G. Tian, Feng Wang
semanticscholar   +1 more source

TOROIDAL FANO VARIETIES AND ROOT SYSTEMS

Mathematics of the USSR-Izvestiya, 1985
A smooth projective variety is called a Fano variety if its anticanonical sheaf is ample. Theorem 1 states that over an algebraically closed field there exist only finitely many mutually nonisomorphic toroidal Fano varieties. Theorem 4 gives a complete classification of toroidal Fano varieties with a centrally symmetric fan.
Voskresenskij, V. E., Klyachko, A. A.
openaire   +1 more source

ON STABILITY OF THE TANGENT BUNDLES OF FANO VARIETIES

International Journal of Mathematics, 1992
\(X\) denotes always a compact Kähler manifold with Kähler form \(\omega\). Let \(E_ 1\), \(E_ 2\) be coherent holomorphic sheaves on \(X\); \(E_ 3\) a coherent sheaf extension of \(E_ 1\) by \(E_ 2\). The pair \((E_ 1,E_ 2)\) is stable (semistable) with respect to the Kähler class \(\omega\) if the generic extension of \(E_ 1\) by \(E_ 2\) is stable ...
openaire   +1 more source