scholarly journals Smooth projective varieties with a torus action of complexity 1 and Picard number 2

2018 ◽  
pp. 611-651
Author(s):  
Anne Fahrner ◽  
Jürgen Hausen ◽  
Michele Nicolussi
Keyword(s):  
Torus Action ◽  
Picard Number ◽  
Projective Varieties ◽  
Smooth Projective Varieties

scholarly journals On the classification of 3-dimensionalSL2(ℂ)-varieties

2000 ◽  
Vol 157 ◽  
pp. 129-147 ◽  
Author(s):  
Stefan Kebekus
Keyword(s):  
Automorphism Group ◽  
Semisimple Group ◽  
Picard Number ◽  
Projective Varieties ◽  
3 Dimensional

In the present work we describe 3-dimensional complexSL2-varieties where the genericSL2-orbit is a surface. We apply this result to classify the minimal 3-dimensional projective varieties with Picard-number 1 where a semisimple group acts such that the generic orbits are 2-dimensional.This is an ingredient of the classification [Keb99] of the 3-dimensional relatively minimal quasihomogeneous varieties where the automorphism group is not solvable.

scholarly journals Schwarzenberger bundles on smooth projective varieties

2016 ◽  
Vol 220 (9) ◽  
pp. 3307-3326 ◽  
Author(s):  
Enrique Arrondo ◽  
Simone Marchesi ◽  
Helena Soares
Keyword(s):  
Projective Varieties ◽  
Smooth Projective Varieties

scholarly journals Abelian Varieties as Automorphism Groups of Smooth Projective Varieties

2018 ◽  
Vol 2020 (7) ◽  
pp. 1942-1956
Author(s):  
Davide Lombardo ◽  
Andrea Maffei
Keyword(s):  
Automorphism Group ◽  
Projective Variety ◽  
Automorphism Groups ◽  
Abelian Varieties ◽  
Smooth Projective Variety ◽  
Projective Varieties ◽  
Smooth Projective Varieties

Abstract We determine which complex abelian varieties can be realized as the automorphism group of a smooth projective variety.

scholarly journals Growth rate of ample heights and the Dynamical Mordell–Lang conjecture

2018 ◽  
Vol 14 (10) ◽  
pp. 2673-2685
Author(s):  
Kaoru Sano
Keyword(s):  
Growth Rate ◽  
Explicit Formula ◽  
Number Fields ◽  
Rational Points ◽  
Positive Answer ◽  
Projective Varieties ◽  
Smooth Projective Varieties

We provide an explicit formula on the growth rate of ample heights of rational points under iteration of endomorphisms of smooth projective varieties over number fields. As an application, we give a positive answer to a variant of the Dynamical Mordell–Lang conjecture for pairs of étale endomorphisms, which is also a variant of the original one stated by Bell, Ghioca, and Tucker in their monograph.

scholarly journals A Riemann–Hurwitz Theorem for the Algebraic Euler Characteristic

2017 ◽  
Vol 60 (3) ◽  
pp. 490-509
Author(s):  
Andrew Fiori
Keyword(s):  
Euler Characteristic ◽  
Euler Characteristics ◽  
Projective Varieties ◽  
Coherent Sheaves ◽  
Irreducible Components ◽  
Arbitrary Dimensions ◽  
Smooth Projective Varieties ◽  
Ramification Locus ◽  
Hurwitz Theorem

AbstractWe prove an analogue of the Riemann–Hurwitz theorem for computing Euler characteristics of pullbacks of coherent sheaves through finite maps of smooth projective varieties in arbitrary dimensions, subject only to the condition that the irreducible components of the branch and ramification locus have simple normal crossings.

A GEOMETRIC VERSION OF DYSON'S LEMMA FOR FACTORS OF ARBITRARY DIMENSION

2002 ◽  
Vol 13 (01) ◽  
pp. 43-65 ◽  
Author(s):  
MARKUS WESSLER
Keyword(s):  
Algebraic Geometry ◽  
Arbitrary Dimension ◽  
Product Theorem ◽  
Projective Varieties ◽  
Quantitative Version ◽  
Weak Positivity ◽  
Projective Lines ◽  
Smooth Projective Varieties ◽  
Geometric Analogue

This paper generalizes the geometric part of the Esnault–Viehweg paper on Dyson's Lemma for a product of projective lines. Using the method of weak positivity from algebraic geometry, we are able to study products of smooth projective varieties of arbitrary dimension and to prove a geometric analogue of Dyson's Lemma for this case. Our main result is in fact a quantitative version of Faltings' product theorem.

scholarly journals Geometric properties of projective manifolds of small degree

2015 ◽  
Vol 160 (2) ◽  
pp. 257-277 ◽  
Author(s):  
SIJONG KWAK ◽  
JINHYUNG PARK
Keyword(s):  
Projective Variety ◽  
Smooth Projective Variety ◽  
Small Degree ◽  
Point Of View ◽  
Geometric Properties ◽  
Projective Varieties ◽  
Cox Rings ◽  
Projective Manifolds ◽  
Simply Connected ◽  
Smooth Projective Varieties

AbstractThe aim of this paper is to study geometric properties of non-degenerate smooth projective varieties of small degree from a birational point of view. First, using the positivity property of double point divisors and the adjunction mappings, we classify smooth projective varieties in $\mathbb{P}$r of degree d ⩽ r + 2, and consequently, we show that such varieties are simply connected and rationally connected except in a few cases. This is a generalisation of P. Ionescu's work. We also show the finite generation of Cox rings of smooth projective varieties in $\mathbb{P}$r of degree d ⩽ r with counterexamples for d = r + 1, r + 2. On the other hand, we prove that a non-uniruled smooth projective variety in $\mathbb{P}$r of dimension n and degree d ⩽ n(r − n) + 2 is Calabi–Yau, and give an example that shows this bound is also sharp.

scholarly journals Rank 3 rigid representations of projective fundamental groups

2018 ◽  
Vol 154 (7) ◽  
pp. 1534-1570 ◽  
Author(s):  
Adrian Langer ◽  
Carlos Simpson
Keyword(s):  
Irreducible Representation ◽  
Projective Variety ◽  
Fundamental Groups ◽  
Projective Varieties ◽  
Smooth Complex ◽  
Complex Projective Variety ◽  
Geometric Origin ◽  
Rank 2 ◽  
Complex Projective ◽  
Smooth Projective Varieties

Let$X$be a smooth complex projective variety with basepoint$x$. We prove that every rigid integral irreducible representation$\unicode[STIX]{x1D70B}_{1}(X\!,x)\rightarrow \operatorname{SL}(3,\mathbb{C})$is of geometric origin, i.e., it comes from some family of smooth projective varieties. This partially generalizes an earlier result by Corlette and the second author in the rank 2 case and answers one of their questions.

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