Non-tautological Hurwitz cycles
نویسندگان
چکیده
Abstract We show that various loci of stable curves sufficiently large genus admitting degree d covers positive define non-tautological algebraic cycles on $${\overline{{\mathcal {M}}}}_{g,N}$$ M ¯ g , N , assuming the non-vanishing -th Fourier coefficient a certain modular form. Our results build those Graber-Pandharipande and van Zelm for 2 elliptic curves; main new ingredient is method to intersect in question with boundary strata, as developed recently by Schmitt-van author.
منابع مشابه
Evaluating tautological classes using only Hurwitz numbers
Hurwitz numbers count ramified covers of a Riemann surface with prescribed monodromy. As such, they are purely combinatorial objects. Tautological classes, on the other hand, are distinguished classes in the intersection ring of the moduli spaces of Riemann surfaces of a given genus, and are thus “geometric.” Localization computations in Gromov-Witten theory provide non-obvious relations betwee...
متن کاملTautological Cycles on Jacobian Varieties
Q containing C and stable with respect to the Fourier transform, the intersection product, the Pontryagin product, pull-backs and push-forwards of multiplication maps by integers. The tautological ring has a mysterious algebraic structure, which has not been completely understood so far. Only recently Beauville proved that R(C) is finite dimensional as a Q-vector space [Be3]. He proved that the...
متن کاملCombinatorics of Tropical Hurwitz Cycles
We study properties of the tropical double Hurwitz loci defined by Bertram, Cavalieri and Markwig. We show that all such loci are connected in codimension one. If we mark preimages of simple ramification points, then for a generic choice of such points the resulting cycles are weakly irreducible, i.e. an integer multiple of an irreducible cycle. We study how Hurwitz cycles can be written as div...
متن کاملOn double Hurwitz numbers with completed cycles
Abstract. In this paper, we collect a number of facts about double Hurwitz numbers, where the simple branch points are replaced by their more general analogues — completed (r + 1)-cycles. In particular, we give a geometric interpretation of these generalised Hurwitz numbers and derive a cut-and-join operator for completed (r+1)-cycles. We also prove a strong piecewise polynomiality property in ...
متن کاملUniversal Algebraic Equivalences between Tautological Cycles on Jacobians of Curves
We present a collection of algebraic equivalences between tautological cycles on the Jacobian J of a curve, i.e., cycles in the subring of the Chow ring of J generated by the classes of certain standard subvarieties of J . These equivalences are universal in the sense that they hold for all curves of given genus. We show also that they are compatible with the action of the Fourier transform on ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2021
ISSN: ['1432-1823', '0025-5874']
DOI: https://doi.org/10.1007/s00209-021-02903-7