TL;DR
This paper constructs a proper moduli space of logarithmic quasimaps relative to a divisor, enabling the definition of numerical invariants that align with existing theories, using advanced logarithmic geometry techniques.
Contribution
It introduces a new proper moduli space for quasimaps relative to divisors in any genus via logarithmic geometry, extending previous theories.
Findings
Constructed a proper Deligne-Mumford stack for logarithmic quasimaps
Established a virtual fundamental class with expected dimension
Derived numerical invariants consistent with Battistella-Nabijou theory
Abstract
We construct a proper moduli space which is a Deligne-Mumford stack parametrising quasimaps relative to a simple normal crossings divisor in any genus using logarithmic geometry. We show this moduli space admits a virtual fundamental class of the expected dimension leading to numerical invariants which agree with the theory of Battistella-Nabijou where the latter is defined.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Commutative Algebra and Its Applications