共查询到20条相似文献,搜索用时 15 毫秒
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M. Cristina Ronconi 《Acta Appl Math》2003,75(1-3):133-150
One of the problems in classifying nonsingular threefolds of general type with p
g
=0 lies in finding the range of the bigenus P
2 (surfaces of general type with p
g
=0 have 2P
210). Another problem involves finding the minimum integer m such that the m-canonical map |mK| is birational for any threefold (m=5 in the case of surfaces). An example of a nonsingular threefold X of general type with q
1=q
2=0, p
g
=P
2=0,P
3=1 is presented. In addition, the m-canonical map of X is birational if and only if m14. The threefold is obtained as a nonsingular model of a degree ten hypersurface in P
4
C
with the affine equation t
2=f
10(x,y,z). 相似文献
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Caryn Werner 《manuscripta mathematica》1994,84(1):327-341
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Masaaki Murakami 《Mathematische Zeitschrift》2006,253(2):251-262
We shall give a bound for the orders of the torsion groups of minimal algebraic surfaces of general type whose first Chern
numbers are twice the Euler characteristics of the structure sheaves minus 1, where the torsion group of a surface is the
torsion part of the Picard group. Namely, we shall show that the order is at most 3 if the Euler characteristic is 2, that
the order is at most 2 if the Euler characteristic is greater than or equal to 3, and that the order is 1 if the Euler characteristic
is greater than or equal to 7. 相似文献
5.
Dominik Burek 《Mathematische Nachrichten》2020,293(4):638-650
Based on Cynk–Hulek method from [7] we construct complex Calabi–Yau varieties of arbitrary dimensions using elliptic curves with an automorphism of order 6. Also we give formulas for Hodge numbers of varieties obtained from that construction. We shall generalize the result of [11] to obtain arbitrarily dimensional Calabi–Yau manifolds which are Zariski in any characteristic . 相似文献
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We construct complex surfaces of general type with and as double covers of Enriques surfaces (called Keum–Naie surfaces) with a different way to the original constructions of Keum and Naie. As a result, we show that there is a -curve on the example with , which might imply a special relation between Keum–Naie surfaces with and . 相似文献
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Rosilde Fimognari Paolo A. Oliverio 《Rendiconti del Circolo Matematico di Palermo》2009,58(1):133-154
We classify minimal smooth surfaces of general type with K
2 = 3, p
g
= 2 which admit a fibration of curves of genus 2.We prove that they form an irreducible set of dimension 22 in their moduli
space.
相似文献
9.
A minimal surface of general type with pg(S) = 0 satisfies 1 K2 9, and it is known that the image of the bicanonical map is a surface for , whilst for , the bicanonical map is always a morphism. In this paper it is shown that is birationalif , and that the degree of is at most 2 if or By presenting two examples of surfaces S with and 8 and bicanonical map of degree 2, it is alsoshown that this result is sharp. The example with is, to our knowledge, a new example of a surfaceof general type with pg = 0. The degree of is also calculated for two other known surfacesof general type with pg = 0 and . In both cases, the bicanonical map turns out to be birational. 相似文献
10.
Minimal complex surfaces of general type with pg = 0 and K2= 7 or 8 whose bicanonical map is not birational are studied.It is shown that if S is such a surface, then the bicanonicalmap has degree 2 (see Bulletin of the London Mathematical Society33 (2001) 110) and there is a fibration f: S P1 suchthat (i) the general fibre F of f is a genus 3 hyperellipticcurve; (ii) the involution induced by the bicanonical map ofS restricts to the hyperelliptic involution of F. Furthermore, if , then f isan isotrivial fibration with six double fibres, and if , then f has five double fibres andit has precisely one fibre with reducible support, consistingof two components. 2000 Mathematics Subject Classification 14J29. 相似文献
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Let S be a smooth minimal projective surface of general type with p_g(S) = q(S) = 1,K_S~2= 6. We prove that the degree of the bicanonical map of S is 1 or 2. So if S has non-birational bicanonical map, then it is a double cover over either a rational surface or a K3 surface. 相似文献
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《Mathematische Nachrichten》2017,290(14-15):2296-2307
We construct simply connected surfaces of general type with invariants and . We use ‐Gorenstein deformations in conjunction with explicit constructions that express the canonical rings by generators and relations. The canonical rings of the surfaces are described as projections. The whole construction is simplified by the use of key varieties based on Steiner 3‐folds. As a consequence of the construction we find two families, each family in a different connected component of the moduli stack , and each linking a Campedelli surface with a Godeaux surface. 相似文献
13.
《Mathematische Nachrichten》2017,290(16):2684-2695
We study a family of surfaces of general type with and , originally constructed by Cancian and Frapporti by using the Computer Algebra System MAGMA . We provide an alternative, computer‐free construction of these surfaces, that allows us to describe their Albanese map and their moduli space. 相似文献
14.
Tomokuni Takahashi 《Mathematische Nachrichten》2013,286(4):402-429
We classify the algebraic surfaces with Eisenbud‐Harris general fibration of genus 4 over a rational curve or an elliptic curve whose slope attains the lower bound. The classification of our surfaces is strongly related to the result of the classification for certain relative quadric hypersurfaces in 3‐dimensional projective space bundles over a rational curve and an elliptic curve. We further prove some results about the canonical maps, the quadric hulls of the canonical images and the deformation for these surfaces. 相似文献
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《Mathematische Nachrichten》2017,290(14-15):2132-2153
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Vicente Lorenzo 《Mathematische Nachrichten》2023,296(6):2503-2512
In this note, the geography of minimal surfaces of general type admitting -actions is studied. More precisely, it is shown that Gieseker's moduli space contains surfaces admitting a -action for every admissible pair such that or . The examples considered allow to prove that the locus of Gorenstein stable surfaces is not closed in the KSBA-compactification of Gieseker's moduli space for every admissible pair such that . 相似文献
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Mustapha Lahyane 《Proceedings of the American Mathematical Society》2005,133(6):1593-1599
A -curve is a smooth rational curve of self-intersection , where is a positive integer. In 1998 Hirschowitz asked whether a smooth rational surface defined over the field of complex numbers, having an anti-canonical divisor not nef and of self-intersection zero, has -curves. In this paper we prove that for such a surface , the set of -curves on is finite but non-empty, and that may have no -curves. Related facts are also considered.