Results 171 to 180 of about 1,118 (197)
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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.
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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.
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Fano Varieties and Fano Polytopes [PDF]
, 2020 The foundation of this thesis is the problem whether a given (normal) Gorenstein Fano variety can be degenerated to a toric Gorenstein Fano variety. We will only consider those degenerations that are compatible with the choice of an ample line bundle on the original variety and an ample rational Cartier divisor on the toric variety.
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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.
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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.
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TOROIDAL FANO VARIETIES AND ROOT SYSTEMS
Mathematics of the USSR-Izvestiya, 1985A 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.
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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 ...
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Special issue on Fano varieties
Rendiconti del Circolo Matematico di Palermo Series 2, 2023Gilberto Bini, Ciro Ciliberto
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Fano varieties in index one Fano complete intersections
Mathematische Zeitschrift, 2007The unirationality of degree \(n\) hypersurfaces of \(\mathbb{P}^n\) is a classical and intricate problem. As suggested by \textit{R. Beheshti} and \textit{J. M. Starr} [J. Algebr. Geom. 17, No. 2, 255--274 (2008; Zbl 1141.14024)], if \(X\) is unirational then it is covered by rational subvarieties of smaller dimension.
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Birationally rigid varieties. I. Fano varieties
Russian Mathematical Surveys, 2007The theory of birational rigidity of rationally connected varieties generalises the classical rationality problem. This paper gives a survey of the current state of this theory and traces its history from Noether's theorem and the Luroth problem to the latest results on the birational superrigidity of higher-dimensional Fano varieties.
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Fano-Varieties of lines on hypersurfaces
Archiv der Mathematik, 1978Barth, W., Van de Ven, A.
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Singularities of linear systems and boundedness of Fano varieties
Annals of Mathematics, 2021Caucher Birkar
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