具有皮卡德数1的素数因子的法诺四倍

IF 0.5 4区数学 Q3 MATHEMATICS

Advances in Geometry Pub Date : 2021-03-30 DOI:10.1515/advgeom-2023-0002

S. A. Secci

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引用次数: 3

摘要

摘要我们在Casagrande和Druel[5]的任意维刻画结果之后，证明了具有Picard数1的素数除数的Picard数3的光滑复Fano四重的分类结果。这些品种是通过炸毁ℙ在Picard数1的光滑Fano变种上沿着余维数2的子变种进行1-回旋。我们详细研究了维度4的情况，并表明它们形成了28个家族。我们计算了主要的数值不变量，确定了反正则系统的基轨迹，并研究了它们的变形，给出了一般成员Kuranishi族的基维数的上界。

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Fano fourfolds having a prime divisor of Picard number 1

Abstract We prove a classification result for smooth complex Fano fourfolds of Picard number 3 having a prime divisor of Picard number 1, after a characterisation result in arbitrary dimension by Casagrande and Druel [5]. These varieties are obtained by blowing-up a ℙ1-bundle over a smooth Fano variety of Picard number 1 along a codimension 2 subvariety. We study in detail the case of dimension 4, and show that they form 28 families. We compute the main numerical invariants, determine the base locus of the anticanonical system, and study their deformations to give an upper bound to the dimension of the base of the Kuranishi family of a general member.

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来源期刊

Advances in Geometry 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.