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DTSTART;TZID=America/New_York:20231106T103000
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UID:10002788-1699266600-1699270200@cmsa.fas.harvard.edu
SUMMARY:Deformations of Landau-Ginzburg models and their fibers
DESCRIPTION:Algebraic Geometry in String Theory Seminar \nSpeaker: Andrew Harder\, Lehigh University \nTitle: Deformations of Landau-Ginzburg models and their fibers \nAbstract: In mirror symmetry\, the dual object to a Fano variety is a Landau-Ginzburg model. Broadly\, a Landau-Ginzburg model is quasi-projective variety Y with a superpotential function w\, but not all such pairs correspond to Fano varieties under mirror symmetry\, so a very natural question to ask is: Which Landau-Ginzburg models are mirror to Fano varieties? In this talk\, I will discuss a cohomological characterization of mirrors of (semi-)Fano varieties\, focusing on the case of threefolds. I’ll discuss how this characterization relates to the deformation and Hodge theory of (Y\,w)\, and in particular\, how the classification of (semi-)Fano threefolds is related to questions about moduli spaces of lattice polarized K3 surfaces.
URL:https://cmsa.fas.harvard.edu/event/agst-11623/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Algebraic Geometry in String Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Algebraic-Geometry-in-String-Theory-11.06.2023.png
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DTSTART;TZID=America/New_York:20231113T103000
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CREATED:20240222T070558Z
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UID:10002787-1699871400-1699875000@cmsa.fas.harvard.edu
SUMMARY:Stacky small resolutions of determinantal octic double solids and noncommutative Gopakumar-Vafa invariants
DESCRIPTION:Algebraic Geometry in String Theory Seminar \n\nSpeaker: Sheldon Katz\, UIUC \nTitle: Stacky small resolutions of determinantal octic double solids and noncommutative Gopakumar-Vafa invariants \nAbstract:  A determinantal octic double solid is the double cover X of P^3 branched along the degree 8 determinant of a symmetric matrix of homogeneous forms on P^3.  These X are nodal CY threefolds which do not admit a projective small resolution.  B-model techniques can be applied to compute GV invariants up to g \le 32.  This raises the question: what is the geometric meaning of these invariants? \nEvidence suggests that these enumerative invariants are associated with moduli stacks of coherent sheaves of modules over a sheaf B of noncommutative algebras on X constructed by Kuznetsov.  One of these moduli stacks is a stacky small resolution X’ of X itself.  This leads to another geometric interpretation of the invariants as being associated with moduli of sheaves on X’ twisted by a Brauer class.  Geometric computations based on these working definitions always agree with the B-model computations. \nThis talk is based on joint work with Albrecht Klemm\, Thorsten Schimannek\, and Eric Sharpe. \n\n 
URL:https://cmsa.fas.harvard.edu/event/agst-111323/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Algebraic Geometry in String Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Algebraic-Geometry-in-String-Theory-11.13.2023.png
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