# Effective cycles on the symmetric product of a curve, I: the diagonal cone

@article{Bastianelli2019EffectiveCO,
title={Effective cycles on the symmetric product of a curve, I: the diagonal cone},
author={Francesco Bastianelli and Alexis Kouvidakis and Angelo Felice Lopez and Filippo Viviani},
journal={Transactions of the American Mathematical Society},
year={2019}
}
• Published 21 November 2017
• Computer Science
• Transactions of the American Mathematical Society
<p>In this paper we investigate the cone <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper P s e f f Subscript n Baseline left-parenthesis upper C Subscript d Baseline right-parenthesis"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>Pseff</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo>⁡<!-- ⁡ --></mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mi>C</mml:mi…
7 Citations

### Effective cycles on the symmetric product of a curve, II: the Abel–Jacobi faces

• Mathematics
Rendiconti Lincei - Matematica e Applicazioni
• 2021
In this paper, which is a sequel of [BKLV], we study the convex-geometric properties of the cone of pseudoeffective $n$-cycles in the symmetric product $C_d$ of a smooth curve $C$. We introduce and

### Cones of special cycles of codimension 2 on orthogonal Shimura varieties

Let X be an orthogonal Shimura variety associated to a unimodular lattice. We investigate the polyhedrality of the cone CX of special cycles of codimension 2 on X. We show that the rays generated by

### Cones of orthogonal Shimura subvarieties and equidistribution

. Let X be an orthogonal Shimura variety, and let C ort r ( X ) be the cone generated by the cohomology classes of orthogonal Shimura subvarieties in X of dimension r . We investigate the asymptotic

### Effective cycles on universal hypersurfaces

. We study the eﬀective cones of cycles on universal hypersurfaces on a projective variety X , particularly focusing on the case of universal hypersurfaces in P n . We determine the eﬀective cones of

### Splitting Brauer classes using the universal Albanese

• Mathematics
L’Enseignement Mathématique
• 2021
We prove that every Brauer class over a field splits over a torsor under an abelian variety. If the index of the class is not congruent to 2 modulo 4, we show that the Albanese variety of any smooth

### Surfaces close to the Severi lines in positive characteristic

Let X be a surface of general type with maximal Albanese dimension over an algebraically closed field of characteristic greater than two: we prove that if K X < 9 2 χ(OX), one has K 2 X ≥

### On the cone of effective surfaces on $\overline{\mathcal A}_3$

• Mathematics
• 2020
We determine five extremal effective rays of the four-dimensional cone of effective surfaces on the toroidal compactification $\overline{\mathcal A}_3$ of the moduli space ${\mathcal A}_3$ of complex