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Alice Garbagnati 《manuscripta mathematica》2013,140(3-4):273-294
The aim of this paper is to construct families of Calabi-Yau threefolds without boundary points with maximal unipotent monodromy and to describe the variation of their Hodge structures. In particular five families are constructed. In all these cases the variation of the Hodge structures of the Calabi-Yau threefolds is basically the variation of the Hodge structures of a family of curves. This allows us to write explicitly the Picard-Fuchs equation for the one-dimensional families. These Calabi-Yau threefolds are desingularizations of quotients of the product of a (fixed) elliptic curve and a K3 surface admitting an automorphisms of order 4 (with some particular properties). We show that these K3 surfaces admit an isotrivial elliptic fibration. 相似文献
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We study the families of lines on the quintic threefolds of the pencilx
0
5
+x
1
5
+x
2
5
+x
3
5
+x
4
5
-5tx
0
x
1
x
2
x
3
x
4=0. We show that on the generic threefold of the pencil there exists a 1-dimensional family of lines that is not a cone.
Partially supported by funds M.P.I. 相似文献
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Michele Rossi 《manuscripta mathematica》1996,89(1):511-544
This paper deals with some families of projective hypersurfaces of degree 6 and dimension 3, left invariant under certain
actions of the group of the cubic roots of unity.
The general Grothendieck-Hodge conjecture, for the families above and for their intersections, is verified. In particular
certain families of elliptic curves on the general element of these families are closely investigated and their degeneration
at the Fermat point is studied. These results are used to verify the general Infinitesimal Hodge Conjecture extending to the
general type case a similar conjecture due to A. Albano and S. Katz.
Research partially supported by italian M.U.R.S.T., by the Science Project “Geom. of Alg. Var.” and by G.N.S.A.G.A. (C.N.R.) 相似文献
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Translated from Matematicheskie Zametki, Vol. 51, No. 1, pp. 114–117, January, 1992. 相似文献
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N. I. Shepherd-Barron 《Compositio Mathematica》1997,105(3):237-265
We show that the birational classification in positive characteristicof smooth Fano threefolds X with Picard number 1 is the same as incharacteristic zero. In particular, there are no exotic such Fanos; asa consequence of the classification, X is shown to be liftable withoutramification to characteristic zero and to contain a line. The maintechniques employed are those of Ekedahl and of Mori and Takeuchi. 相似文献
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A. G. Kuznetsov 《Proceedings of the Steklov Institute of Mathematics》2009,264(1):110-122
We consider the structure of the derived categories of coherent sheaves on Fano threefolds with Picard number 1 and describe
a strange relation between derived categories of different threefolds. In the appendix we discuss how the ring of algebraic
cycles of a smooth projective variety is related to the Grothendieck group of its derived category.
Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2009, Vol. 264, pp. 116–128.
In memory of V.A. Iskovskikh 相似文献
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Marc Levine 《Mathematische Annalen》1983,262(3):391-406
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Vo Van Tan 《manuscripta mathematica》1990,69(1):333-338
In contrast with the 2-dimensional case, we would like to exhibit here an example of a compactifiable strongly pseudoconvex
threefold X such that a) the analytic Kodaira dimension κ(X)=3 and b) its exceptional subvariety S is projective algebraic;
yet X is not quasi-projective. 相似文献
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For any smooth quartic threefold in P4 we classify pencils on it whose general element is an irreducible surface birational to a surface of Kodaira dimension zero. 相似文献
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Emilia Mezzetti Dario Portelli 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2000,70(1):211-238
A classification theorem is given of projective threefolds that are covered by the lines of a two-dimensional family, but
not by a higher dimensional family. Precisely, ifX is such a threefold, let Σ denote the Fano scheme of lines onX and μ the number of lines contained inX and passing through a general point ofX. Assume that Σ is generically reduced. Then μ ≤ 6. Moreover,X is birationally a scroll over a surface (μ = 1), orX is a quadric bundle, orX belongs to a finite list of threefolds of degree at most 6. The smooth varieties of the third type are precisely the Fano
threefolds with −K
X
= 2H
X
.
This work has been done in the framework of the activities of EAGER. Both authors have been supported by funds of MURST, Progetto
Geometria Algebrica, Algebra Commutativa e Aspetti Computazionali.
The paper has been widely improved while the second author was guest at the University of Oslo. The financial support from
both the University of Oslo and the Norwegian Research Council is gratefully aknowledged. 相似文献