37 citations · 164 across the 30 of their papers we have counts for
45 papers
The GW/PT conjectures for toric pairs
Davesh Maulik, Dhruv Ranganathan
We prove the conjectural correspondence between logarithmic Gromov-Witten theory and logarithmic Donaldson/Pandharipande-Thomas theory for pairs consisting of a to…
An invitation to the enumerative geometry of degenerations
Dhruv Ranganathan
This expository article is an introduction to logarithmic Gromov--Witten (GW) theory. We discuss how to study the GW theory of a smooth projective variety via simple normal crossin…
Gromov-Witten theory, degenerations, and the tautological ring
Davesh Maulik, Dhruv Ranganathan
Gromov-Witten (GW) theory produces Chow and cohomology classes on the moduli of curves, and there are several conjectures/speculations about their relation to the tautological ring…
Logarithmic Quot spaces, boundedness, and K-tropicalizations
Patrick Kennedy-Hunt, Dhruv Ranganathan
Logarithmic Hilbert and Quot spaces are generalizations of their traditional versions adapted to study pairs and degenerations. The logarithmic Quot spaces of parameterize…
The many faces of a logarithmic scheme
Thibault Poiret, Dhruv Ranganathan
A standard assumption in the study of logarithmic structures is "fineness", but this assumption is not preserved by intersections, fiber products, and more general limits. We expla…
Logarithmic tautological rings of the moduli spaces of curves
Rahul Pandharipande, Dhruv Ranganathan, Johannes Schmitt +1
We define the logarithmic tautological rings of the moduli spaces of Deligne-Mumford stable curves (together with a set of additive generators lifting the decorated strata classes…
Combinatorics of Hurwitz degenerations and tropical realizability
Mia Lam, Chi Kin Ng, Dhruv Ranganathan
We investigate the realizability of balanced functions on tropical curves, establishing new sufficient criteria for superabundant functions on genus two curves, analogous to the we…
Logarithmic negative tangency and root stacks
Luca Battistella, Navid Nabijou, Dhruv Ranganathan
We study stable maps to normal crossings pairs with possibly negative tangency orders. There are two independent models: punctured Gromov-Witten theory of pairs and orbifold Gromov…
Logarithmic enumerative geometry for curves and sheaves
Davesh Maulik, Dhruv Ranganathan
We propose a logarithmic enhancement of the Gromov-Witten/Donaldson-Thomas correspondence, with descendants, and study its behavior under simple normal crossings degenerations. The…
Counting tropical curves in : computation & polynomiality properties
Daniel Corey, Hannah Markwig, Dhruv Ranganathan
Counts of curves in with fixed contact order with the toric boundary and satisfying point conditions can be determined with tropical methods by Mik…
Logarithmic Gromov-Witten theory and double ramification cycles
Dhruv Ranganathan, Ajith Urundolil Kumaran
We examine the logarithmic Gromov-Witten cycles of a toric variety relative to its full toric boundary. The cycles are expressed as products of double ramification cycles and natur…
Pluricanonical cycles and tropical covers
Renzo Cavalieri, Hannah Markwig, Dhruv Ranganathan
We extract a system of numerical invariants from logarithmic intersection theory on pluricanonical double ramification cycles, and show that these invariants exhibit a number of pr…
Gromov-Witten theory via roots and logarithms
Luca Battistella, Navid Nabijou, Dhruv Ranganathan
Orbifold and logarithmic structures provide independent routes to the virtual enumeration of curves with tangency orders for a simple normal crossings pair . The theories do…
Gromov-Witten theory and invariants of matroids
Dhruv Ranganathan, Jeremy Usatine
We use techniques from Gromov-Witten theory to construct new invariants of matroids taking value in the Chow groups of spaces of rational curves in the permutohedral toric variety.…
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…
Logarithmic Donaldson-Thomas theory
Davesh Maulik, Dhruv Ranganathan
Let be a smooth threefold with a simple normal crossings divisor . We construct the Donaldson-Thomas theory of the pair enumerating ideal sheaves on relative to…
A note on the cycle of curves in a product of pairs
Dhruv Ranganathan
We prove that the cycle-valued logarithmic Gromov--Witten theory of a product of simple normal crossings pairs decomposes into a product of pieces coming from and $…
Gromov-Witten theory with maximal contacts
Navid Nabijou, Dhruv Ranganathan
We propose an intersection-theoretic method to reduce questions in genus zero logarithmic Gromov-Witten theory to questions in the Gromov-Witten theory of smooth pairs, in the pres…
Curve counting in genus one: elliptic singularities & relative geometry
Luca Battistella, Navid Nabijou, Dhruv Ranganathan
We construct and study the reduced, relative, genus one Gromov--Witten theory of very ample pairs. These invariants form the principal component contribution to relative Gromov--Wi…
Logarithmic Gromov-Witten theory with expansions
Dhruv Ranganathan
We construct relative Gromov--Witten theory with expanded degenerations in the normal crossings setting and establish a degeneration formula for the resulting invariants. Given a s…
Rational curves in the logarithmic multiplicative group
Dhruv Ranganathan, Jonathan Wise
The logarithmic multiplicative group is a proper group object in logarithmic schemes, which morally compactifies the usual multiplicative group. We study the structure of the stack…
Motivic Hilbert zeta functions of curves are rational
Dori Bejleri, Dhruv Ranganathan, Ravi Vakil
The motivic Hilbert zeta function of a variety is the generating function for classes in the Grothendieck ring of varieties of Hilbert schemes of points of the variety. In this pap…
Moduli of stable maps in genus one and logarithmic geometry II
Dhruv Ranganathan, Keli Santos-Parker, Jonathan Wise
This is the second in a pair of papers developing a framework to apply logarithmic methods in the study of singular curves of genus . This volume focuses on logarithmic Gromov--…
Incidence geometry and universality in the tropical plane
Milo Brandt, Michelle Jones, Catherine Lee +1
We examine the incidence geometry of lines in the tropical plane. We prove tropical analogs of the Sylvester-Gallai and Motzkin-Rabin theorems in classical incidence geometry. This…