scholarly journals Log -modules and index theorems

2021 ◽  
Vol 9 ◽  
Author(s):  
Lei Wu ◽  
Peng Zhou
Keyword(s):  
Comparison Theorem ◽  
Index Theorem ◽  
Perverse Sheaves ◽  
Projective Varieties ◽  
Type Formula ◽  
Index Theorems ◽  
De Rham ◽  
Smooth Projective Varieties

Abstract We study log $\mathscr {D}$ -modules on smooth log pairs and construct a comparison theorem of log de Rham complexes. The proof uses Sabbah’s generalized b-functions. As applications, we deduce a log index theorem and a Riemann-Roch type formula for perverse sheaves on smooth quasi-projective varieties. The log index theorem naturally generalizes the Dubson-Kashiwara index theorem on smooth projective varieties.

scholarly journals Index theorem for non-supersymmetric fermions coupled to a non-Abelian string and electric charge quantization

2018 ◽  
Vol 33 (09) ◽  
pp. 1850053
Author(s):  
M. Shifman ◽  
A. Yung
Keyword(s):  
Gauge Group ◽  
Electric Charge ◽  
Index Theorem ◽  
Index Theorems ◽  
Zero Modes ◽  
Left Handed ◽  
Charge Quantization ◽  
Supersymmetric Theories ◽  
String Background

Non-Abelian strings are considered in non-supersymmetric theories with fermions in various appropriate representations of the gauge group U[Formula: see text]. We derive the electric charge quantization conditions and the index theorems counting fermion zero modes in the string background both for the left-handed and right-handed fermions. In both cases we observe a non-trivial [Formula: see text] dependence.

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.

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