The tautological ring of
Mehdi Tavakol (2011)
Annales de l’institut Fourier
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We describe the tautological ring of the moduli space of stable -pointed curves of genus one of compact type. It is proven that it is a Gorenstein algebra.
Mehdi Tavakol (2011)
Annales de l’institut Fourier
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We describe the tautological ring of the moduli space of stable -pointed curves of genus one of compact type. It is proven that it is a Gorenstein algebra.
Andrea Bruno, Massimiliano Mella (2013)
Journal of the European Mathematical Society
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The paper studies fiber type morphisms between moduli spaces of pointed rational curves. Via Kapranov’s description we are able to prove that the only such morphisms are forgetful maps. This allows us to show that the automorphism group of is the permutation group on elements as soon as .
Carel Faber, Sergey Shadrin, Dimitri Zvonkine (2010)
Annales scientifiques de l'École Normale Supérieure
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In [11], A. Givental introduced a group action on the space of Gromov–Witten potentials and proved its transitivity on the semi-simple potentials. In [24, 25], Y.-P. Lee showed, modulo certain results announced by C. Teleman, that this action respects the tautological relations in the cohomology ring of the moduli space of stable pointed curves. Here we give a simpler proof of this result. In particular, it implies that in any semi-simple Gromov–Witten theory where arbitrary correlators...
Gavril Farkas, Katharina Ludwig (2010)
Journal of the European Mathematical Society
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We study the enumerative geometry of the moduli space of Prym varieties of dimension . Our main result is that the compactication of is of general type as soon as and is different from 15. We achieve this by computing the class of two types of cycles on : one defined in terms of Koszul cohomology of Prym curves, the other defined in terms of Raynaud theta divisors associated to certain vector bundles on curves. We formulate a Prym–Green conjecture on syzygies of Prym-canonical...
Gilberto Bini, John Harer (2011)
Journal of the European Mathematical Society
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Let be the moduli space of -pointed Riemann surfaces of genus . Denote by the Deligne-Mumford compactification of . In the present paper, we calculate the orbifold and the ordinary Euler characteristic of for any and such that .
Patrick Brosnan, Zinovy Reichstein, Angelo Vistoli (2011)
Journal of the European Mathematical Society
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In this paper we consider questions of the following type. Let be a base field and be a field extension. Given a geometric object over a field (e.g. a smooth curve of genus ), what is the least transcendence degree of a field of definition of over the base field ? In other words, how many independent parameters are needed to define ? To study these questions we introduce a notion of essential dimension for an algebraic stack. Using the resulting theory, we give a complete...
Nazar Arakelian, Herivelto Borges (2015)
Acta Arithmetica
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For each integer s ≥ 1, we present a family of curves that are -Frobenius nonclassical with respect to the linear system of plane curves of degree s. In the case s=2, we give necessary and sufficient conditions for such curves to be -Frobenius nonclassical with respect to the linear system of conics. In the -Frobenius nonclassical cases, we determine the exact number of -rational points. In the remaining cases, an upper bound for the number of -rational points will follow from Stöhr-Voloch...
Z. Ditzian, S. Tikhonov (2007)
Studia Mathematica
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Relations between moduli of smoothness of the derivatives of a function and those of the function itself are investigated. The results are for and for 0 < p < ∞ using the moduli of smoothness and respectively.
Michael Hutchings (2002)
Journal of the European Mathematical Society
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Let be a surface with a symplectic form, let be a symplectomorphism of , and let be the mapping torus of . We show that the dimensions of moduli spaces of embedded pseudoholomorphic curves in , with cylindrical ends asymptotic to periodic orbits of or multiple covers thereof, are bounded from above by an additive relative index. We deduce some compactness results for these moduli spaces. This paper establishes some of the foundations for a program with Michael Thaddeus, to...
Tomasz Jędrzejak (2008)
Bulletin of the Polish Academy of Sciences. Mathematics
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We study the family of curves , where p is an odd prime and m is a pth power free integer. We prove some results about the distribution of root numbers of the L-functions of the hyperelliptic curves associated to the curves . As a corollary we conclude that the jacobians of the curves with even analytic rank and those with odd analytic rank are equally distributed.
Alexander Schmitt (2005)
Journal of the European Mathematical Society
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In the present paper, we give a first general construction of compactified moduli spaces for semistable -bundles on an irreducible complex projective curve with exactly one node, where is a semisimple linear algebraic group over the complex numbers.
Enrica Floris (2013)
Annales de l’institut Fourier
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In this work we study the moduli part in the canonical bundle formula of an lc-trivial fibration whose general fibre is a rational curve. If is the Cartier index of the fibre, it was expected that would provide a bound on the denominators of the moduli part. Here we prove that such a bound cannot even be polynomial in , we provide a bound and an example where the smallest integer that clears the denominators of the moduli part is . Moreover we prove that even locally the denominators...
Daniele Arcara, Aaron Bertram (2013)
Journal of the European Mathematical Society
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We give a one-parameter family of Bridgeland stability conditions on the derived category of a smooth projective complex surface and describe “wall-crossing behavior” for objects with the same invariants as when generates Pic and . If, in addition, is a or Abelian surface, we use this description to construct a sequence of fine moduli spaces of Bridgeland-stable objects via Mukai flops and generalized elementary modifications of the universal coherent sheaf. We also discover...
Lj. Protić, N. Bokan (1980)
Matematički Vesnik
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Carlos Matheus, Gabriela Weitze-Schmithüsen (2013)
Bulletin de la Société Mathématique de France
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We construct an explicit family of arithmetic Teichmüller curves , , supporting -invariant probabilities such that the associated -representation on has complementary series for every . Actually, the size of the spectral gap along this family goes to zero. In particular, the Teichmüller geodesic flow restricted to these explicit arithmetic Teichmüller curves has arbitrarily slow rate of exponential mixing.
David Ben-Zvi, Thomas Nevins (2011)
Journal of the European Mathematical Society
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We study the geometry of -bundles—locally projective -modules—on algebraic curves, and apply them to the study of integrable hierarchies, specifically the multicomponent Kadomtsev–Petviashvili (KP) and spin Calogero–Moser (CM) hierarchies. We show that KP hierarchies have a geometric description as flows on moduli spaces of -bundles; in particular, we prove that the local structure of -bundles is captured by the full Sato Grassmannian. The rational, trigonometric, and elliptic solutions...
Tomas Edlund (2004)
Annales Polonici Mathematici
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It is shown that there exist functions on the boundary of the unit disk whose graphs are complete pluripolar. Moreover, for any natural number k, such functions are dense in the space of functions on the boundary of the unit disk. We show that this result implies that the complete pluripolar closed curves are dense in the space of closed curves in ℂⁿ. We also show that on each closed subset of the complex plane there is a continuous function whose graph is complete pluripolar. ...
Nicola Pagani (2013)
Annales de l’institut Fourier
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In this work we compute the Chen–Ruan cohomology of the moduli spaces of smooth and stable -pointed curves of genus . In the first part of the paper we study and describe stack theoretically the twisted sectors of and . In the second part, we study the orbifold intersection theory of . We suggest a definition for an orbifold tautological ring in genus , which is a subring of both the Chen–Ruan cohomology and of the stringy Chow ring.
Michael Stoll (2011)
Journal de Théorie des Nombres de Bordeaux
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This is an extended version of an invited lecture I gave at the Journées Arithmétiques in St. Étienne in July 2009. We discuss the state of the art regarding the problem of finding the set of rational points on a (smooth projective) geometrically integral curve over . The focus is on practical aspects of this problem in the case that the genus of is at least , and therefore the set of rational points is finite.