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Izv. Akad. Nauk SSSR Ser. Mat., 1985, Volume 49, Issue 2, Pages 445–459 (Mi izv1362)  

On some numerical characteristics of multidimensional Fano varieties

V. V. Batyrev


Abstract: On the basis of homological properties of the homogeneous coordinate ring $R(V)$ of an $n$-dimensional projective Fano variety $V$ over the field $\mathbf C$ estimates are obtained for the degrees of generators of the algebra $R(V)$ and the ideal $I(V)$. All possible values are found for the dimension and the degree of a variety $V$ of codimension 3 in $\mathbf P^N$ which is not a complete intersection. We give a description of multidimensional Fano varieties of codimension 4 in $\mathbf P^N$ whose linear sections are canonical curves of genus 6.
Bibliography: 12 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1986, 26:2, 423–435

Bibliographic databases:

UDC: 512.7
MSC: Primary 14J40, 14M07; Secondary 13H10, 14C20
Received: 25.10.1983

Citation: V. V. Batyrev, “On some numerical characteristics of multidimensional Fano varieties”, Izv. Akad. Nauk SSSR Ser. Mat., 49:2 (1985), 445–459; Math. USSR-Izv., 26:2 (1986), 423–435

Citation in format AMSBIB
\Bibitem{Bat85}
\by V.~V.~Batyrev
\paper On~some numerical characteristics of multidimensional Fano varieties
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1985
\vol 49
\issue 2
\pages 445--459
\mathnet{http://mi.mathnet.ru/izv1362}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=791311}
\zmath{https://zbmath.org/?q=an:0593.14025}
\transl
\jour Math. USSR-Izv.
\yr 1986
\vol 26
\issue 2
\pages 423--435
\crossref{https://doi.org/10.1070/IM1986v026n02ABEH001154}


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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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