اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn the crossroads of enumerative geometry and geometric representation theory
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Andrei Okounkov
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The subjects in the title are interwoven in many different and very deep ways. I recently wrote several expository accounts [64-66] that reflect a certain range of developments, but even in their totality they cannot be taken as a comprehensive survey. In the format of a 30-page contribution aimed at a general mathematical audience, I have decided to illustrate some of the basic ideas in one very interesting example - that of HilbpC2, nq, hoping to spark the curiosity of colleagues in those numerous fields of study where one should expect applications.
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This is an introduction to: (1) the enumerative geometry of rational curves in equivariant symplectic resolutions, and (2) its relation to the structures of geometric representation theory. Written for the 2015 Algebraic Geometry Summer Institute.
The polynomial ring $B_r:=mathbb{Q}[e_1,ldots,e_r]$ in $r$ indeterminates is a representation of the Lie algebra of all the endomorphism of $mathbb{Q}[X]$ vanishing at powers $X^j$ for all but finitely many $j$. We determine a $B_r$-valued formal pow
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