Logarithmic moduli of roots of line bundles on curves

Holmes, David R.; Orecchia, Giulio

doi:10.48550/arxiv.2201.06869

Cited by 2 publications

(3 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Equation (42) follows from the codimension g part of (41) together with [5]. 32 Here, η Pic denotes the universal class on Pic from Section 6.3.…”

Section: The Formulamentioning

confidence: 99%

See 1 more Smart Citation

Logarithmic intersections of double ramification cycles

Holmes¹,

Schwarz²

2022

Alg. Geom.

Self Cite

View full text Add to dashboard Cite

Let A = (a 1 , . . . , a n ) be a vector of integers which sum to k(2g − 2 + n). The double ramification cycle DR g,A ∈ CH g (M g,n ) on the moduli space of curves is the virtual class of an Abel-Jacobi locus of pointed curves (C, x 1 , . . . , x n ) satisfyingThe Abel-Jacobi construction requires log blow-ups of M g,n to resolve the indeterminacies of the Abel-Jacobi map. Holmes [29] has shown that DR g,A admits a canonical lift logDR g,A ∈ logCH g (M g,n ) to the logarithmic Chow ring, which is the limit of the intersection theories of all such blow-ups.The main result of the paper is an explicit formula for logDR g,A which lifts Pixton's formula for DR g,A . The central idea is to study the universal Jacobian over the moduli space of curves (following Caporaso [12], Kass-Pagani [37], and Abreu-Pacini [3]) for certain stability conditions. Using the criterion of Holmes-Schwarz [34], the universal double ramification theory of Bae-Holmes-Pandharipande-Schmitt-Schwarz [5] applied to the universal line bundle determines the logarithmic double ramification cycle. The resulting formula, written in the language of piecewise polynomials, depends upon the stability condition (and admits a wall-crossing study). Several examples are computed.

show abstract

“…Equation (42) follows from the codimension g part of (41) together with [5]. 32 Here, η Pic denotes the universal class on Pic from Section 6.3.…”

Section: The Formulamentioning

confidence: 99%

“…We refer the reader to [5, Section 0], [35, Section 0], and [55, Section 5] for more leisurely introductions to the subject of double ramification cycles. For a sampling of the development and application of the theory in a variety of directions, see [4,5,9,10,11,15,18,19,20,25,30,32,33,35,36,47,48,51,57,58,60].…”

Section: Introduction 1double Ramification Cyclesmentioning

confidence: 99%

Logarithmic intersections of double ramification cycles

Holmes¹,

Schwarz²

2022

Alg. Geom.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The compactifications are a fundamental tool in the computation of the double ramification cycle (see for example [JPPZ17]). For a recent generalization of the work of Chiodo and Jarvis with applications to the double ramification cycle, see [HO22].…”

Section: Introductionmentioning

confidence: 99%

On moduli spaces of roots in algebraic and tropical geometry

Abreu¹,

Pacini²,

Secco³

2022

Preprint

View full text Add to dashboard Cite

In this paper we construct a tropical moduli space parametrizing roots of divisors on tropical curves. We study the relation between this space and the skeleton of Jarvis moduli space of nets of limit roots on stable curves. We show that the combinatorics of the moduli space of tropical roots is governed by the poset of flows, a poset parametrizing certain flows on graphs. We show many properties of connectedness of this poset and generalize some results on linkage of graphs. We compare our results with recent results about the tropicalization of the space of admissible covers.

show abstract

Logarithmic moduli of roots of line bundles on curves

Cited by 2 publications

References 11 publications

Logarithmic intersections of double ramification cycles

Logarithmic intersections of double ramification cycles

On moduli spaces of roots in algebraic and tropical geometry

Contact Info

Product

Resources

About