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Crossing the wall: Branes vs. bundles
"... Abstract: We test a recently proposed wallcrossing formula for the change of the Hilbert space of BPS states in d = 4, N = 2 theories. We study decays of D4D2D0 systems into pairs of D4D2D0 systems and we show how the wallcrossing formula reproduces results of Göttsche and Yoshioka on wallcrossin ..."
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Abstract: We test a recently proposed wallcrossing formula for the change of the Hilbert space of BPS states in d = 4, N = 2 theories. We study decays of D4D2D0 systems into pairs of D4D2D0 systems and we show how the wallcrossing formula reproduces results of Göttsche and Yoshioka on wallcrossing behavior of the moduli of slopestable holomorphic bundles over holomorphic surfaces. Our comparison shows very clearly that the moduli space of the D4D2D0 system on a rigid surface in a CalabiYau is not the same as the moduli space of torsion free sheaves, even when worldhseet instantons are neglected. Moreover, we argue that the physical formula should make some new mathematical predictions for a
REFINED CURVE COUNTING ON COMPLEX SURFACES
, 2012
"... We define refined invariants which “count” nodal curves in sufficiently ample linear systems on surfaces, conjecture that their generating function is multiplicative, and conjecture explicit formulas in the case of K3 and abelian surfaces. We also give a refinement of the CaporasoHarris recursion ..."
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Cited by 5 (3 self)
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We define refined invariants which “count” nodal curves in sufficiently ample linear systems on surfaces, conjecture that their generating function is multiplicative, and conjecture explicit formulas in the case of K3 and abelian surfaces. We also give a refinement of the CaporasoHarris recursion, and conjecture that it produces the same invariants in the sufficiently ample setting. The refined recursion specializes at y = −1 to the ItenbergKharlamovShustin recursion for Welschinger invariants. We find similar interactions between refined invariants of individual curves and real invariants of their versal families.
1ELLIPTIC GENERA, REAL ALGEBRAIC VARIETIES AND QUASIJACOBI FORMS
"... Abstract. This paper surveys the push forward formula for elliptic class and various applications obtained in the papers by L.Borisov and the author. In the remaining part we discuss the ring of quasiJacobi forms which allows to characterize the functions which are the elliptic genera of almost com ..."
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Abstract. This paper surveys the push forward formula for elliptic class and various applications obtained in the papers by L.Borisov and the author. In the remaining part we discuss the ring of quasiJacobi forms which allows to characterize the functions which are the elliptic genera of almost complex manifolds and extension of Ochanine elliptic genus to certain singular real algebraic varieties.