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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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Birationally rigid Fano varieties
Russian Mathematical Surveys, 2005The birational superrigidity and, in particular, the non-rationality of a smooth three-dimensional quartic was proved by V. Iskovskikh and Yu. Manin in 1971, and this led immediately to a counterexample to the three-dimensional Luroth problem. Since then, birational rigidity and superrigidity have been proved for a broad class of higher-dimensional ...
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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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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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Current and future cancer staging after neoadjuvant treatment for solid tumors
Ca-A Cancer Journal for Clinicians, 2021James D Brierley Mb, Frcp +1 more
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Fano-Varieties of lines on hypersurfaces
Archiv der Mathematik, 1978Barth, W., Van de Ven, A.
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Soft actuators for real-world applications
Nature Reviews Materials, 2021Meng Li, Aniket Pal, Amirreza Aghakhani
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Exercise is medicine in oncology: Engaging clinicians to help patients move through cancer
Ca-A Cancer Journal for Clinicians, 2019Kathryn H Schmitz +2 more
exaly