arXiv subjects

Georgios Politopoulos

Publications and source records attributed to Georgios Politopoulos.

4 recordsLinked to original sources

arXiv2026

Spin volumes of minimal strata and Chiodo integrals

We derive a closed formula for the Masur-Veech volumes of spin-parity components of the stratum of abelian differentials with a single zero of maximal order. Our approach is based on the intersection theory of the virtual subcone of spin-parity squares inside the Hodge bundle, recently developed by Holmes-Politopoulos-Sauvaget. This is a spin refinement of a classical result of Sauvaget and agrees with the lattice-point counting technique of Chen-M\"oller-Sauvaget-Zagier. We further apply this theory to compute spin counterparts of virtual volumes, defined recently by Sauvaget. These virtual volumes are related to area Siegel-Veech constants and we are able to compute these invariants component-wise. In addition, by comparing our method for non-parity squares with the classical result of Sauvaget, we compute specific Chiodo integrals.

math.AG↗

arXiv2025

DR cycles and strata of differentials with spin parity

We study classes of strata of differentials with fixed spin parity in the Chow ring of moduli spaces of curves. We show that these classes are tautological and computable. Furthermore, we establish the refined DR cycle formula for these classes.

math.AG↗

arXiv2022

Relations for quadratic Hodge integrals via stable maps

Following Faber-Pandharipande, we use the virtual localization formula for the moduli space of stable maps to $ \mathbb{P}^1 $ to compute relations between Hodge integrals. We prove that certain generating series of these integrals are polynomials.

math.AG↗

arXiv2022

Computation of $\lambda$-classes via strata of differentials

We introduce a new family of tautological relations of the moduli space of stable curves of genus $g$. These relations are obtained by computing the Poincar\'e-dual class of empty loci in the Hodge bundle. We use these relations to obtain a new expression for the Chern classes of the Hodge bundle. We prove that the $(g-i)$th class can be expressed as a linear combination of tautological classes involving only stable graphs with at most $i$ loops. In particular the top Chern class may be expressed with trees. This property was expected as a consequence of the DR/DZ equivalence conjecture by Buryak-Gu\'er\'e-Rossi.

math.AG↗