11 citations · 47 across the 15 of their papers we have counts for
19 papers · 1 filter
Hodge integrals on admissible covers and tautological projections of Prym classes
Yoav Len, Sam Molcho, Navid Nabijou
In the moduli space of abelian varieties, Prym loci parametrise Prym varieties associated to covers of curves with fixed degree and monodromy data. We derive and implement an algor…
Weight decomposition for toroidal abelian fibrations
Younghan Bae, Jeremy Feusi, Aitor Iribar Lopez +1
We study the action of the rational multiplication by map on the Chow groups of degenerations of principally polarized abelian varieties of torus rank at most one, as well as i…
Birational Classification of Orbifold Compactified Jacobians
Jeremy Feusi, Sam Molcho
We study the equivariant orbifold birational classification problem for families of toroidal compactifications of a group over a toroidal base, in the cases where is an alg…
Fourier transforms and Abel-Jacobi theory
Younghan Bae, Sam Molcho, Aaron Pixton
We relate Fourier transforms between compactified Jacobians over the moduli space of stable curves to logarithmic Abel-Jacobi theory. As an application, we compute the pushforward…
Tautological projection for cycles on the moduli space of abelian varieties
Samir Canning, Sam Molcho, Dragos Oprea +1
We define a tautological projection operator for algebraic cycle classes on the moduli space of principally polarized abelian varieties : every cycle class decompose…
Remarks on logarithmic étale sheafification
Samouil Molcho, Jonathan Wise
We prove criteria for a presheaf on logarithmic schemes to be a sheaf in the full logarithmic étale topology and describe several situations where the structure sheaf and logarithm…
Smooth Compactifications of the Abel-Jacobi Section
Sam Molcho
For a small generic universal stability condition of degree and a vector of integers adding up to , the spaces resolving the Abel-Jacobi…
Pullbacks of Brill-Noether Classes Under Abel-Jacobi Sections
Sam Molcho
We prove that the pullbacks of the virtual fundamental classes of the Brill-Noether loci under any Abel-Jacobi section lie in the tautological ring of the moduli space of stable cu…
Logarithmic double ramification cycles
D. Holmes, S. Molcho, R. Pandharipande +2
Let be a vector of integers which sum to . The double ramification cycle on the moduli spac…
Tropicalization of the universal Jacobian
Margarida Melo, Samouil Molcho, Martin Ulirsch +1
In this article we provide a stack-theoretic framework to study the universal tropical Jacobian over the moduli space of tropical curves. We develop two approaches to the process o…
A case study of intersections on blowups of the moduli of curves
Sam Molcho, Dhruv Ranganathan
We explain how logarithmic structures select principal components in an intersection of schemes. These manifest in Chow homology and can be understood using strict transforms under…
The Hodge bundle, the universal 0-section, and the log Chow ring of the moduli space of curves
Samouil Molcho, Rahul Pandharipande, Johannes Schmitt
We bound from below the complexity of the top Chern class of the Hodge bundle in the Chow ring of the moduli space of curves: no formulas in terms of classes of degrees 1 and 2 can…
Models of Jacobians of curves
David Holmes, Samouil Molcho, Giulio Orecchia +1
We show that the Jacobians of prestable curves over toroidal varieties always admit Néron models. These models are rarely quasi-compact or separated, but we also give a complete cl…
Logarithmically Regular Morphisms
Sam Molcho, Michael Temkin
We consider the stack parametrizing log schemes over a log scheme , and weak and strong properties of log morphisms via , as defined by Olsson…
The logarithmic Picard group and its tropicalization
Samouil Molcho, Jonathan Wise
We construct the logarithmic and tropical Picard groups of a family of logarithmic curves and realize the latter as the quotient of the former by the algebraic Jacobian. We show th…
Universal Weak Semistable Reduction
Sam Molcho
We show that a toroidal morphism can be reduced to a weakly semistable one in a universal way if we allow families to be modified to Deligne-Mumford stacks instead of schemes.
A Theory of Stacky Fans
W. D. Gillam, Sam Molcho
We study the category of KM fans - a "stacky" generalization of the category of fans considered in toric geometry - and its various realization functors to "geometric" categories.…
Logarithmic stable toric varieties and their moduli
Kenneth Ascher, Samouil Molcho
The Chow quotient of a toric variety by a subtorus, as defined by Kapranov-Sturmfels-Zelevinsky, coarsely represents the main component of the moduli space of stable toric varietie…
Localization for logarithmic stable maps
Samouil Molcho, Evangelos Routis
We prove a virtual localization formula for Bumsig Kim's space of logarithmic stable maps. The formula is closely related and can in fact recover the relative virtual localization…