Titlebook: Geometry of Moduli; Jan Arthur Christophersen,Kristian Ranestad Conference proceedings 2018 Springer Nature Switzerland AG 2018 algebraic

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Stratifying Quotient Stacks and Moduli Stacks,.∕.], where . is a projective scheme and . is a linear algebraic group with internally graded unipotent radical acting linearly on ., in such a way that each stratum [.∕.] has a geometric quotient .∕.. This leads to stratifications of moduli stacks (for example, sheaves over a projective scheme) such that each stratum has a coarse moduli space.

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The Moduli Spaces of Sheaves on Surfaces, Pathologies and Brill-Noether Problems,rill-Noether problem for rational surfaces. In order to highlight some of the difficulties for more general surfaces, we show that moduli spaces of rank 2 sheaves on very general hypersurfaces of degree . in . can have arbitrarily many irreducible components as . tends to infinity.

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Geometric Invariant Theory of Syzygies, with Applications to Moduli Spaces,ed to make some progress in this program, that of polarized K3 surfaces of odd genus, and of genus six canonical curves. Applications of our results include effectivity statements for divisor classes on the moduli space of odd genus K3 surfaces, and a new construction in the Hassett-Keel program for the moduli space of genus six curves.

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Jan Arthur Christophersen,Kristian RanestadFirst publication of surveys on recent developments on moduli spaces in algebraic geometry.Comprehensive collection.Will serve both as a reference and a guide to important directions in the geometric

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Torben Kuhlenkasper,Andreas Handl case of where the fibration is .?×?., the product of a .3 surface and an elliptic curve. Oberdieck and Pandharipande conjectured (Oberdieck and Pandharipande, ., Progress in Mathematics, vol. 315 (Birkh?user/Springer, Cham, 2016), pp. 245–278, arXiv:math/1411.1514) that the partition function of th

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