{"product_id":"9788876425585","title":"Rigid Germs, the Valuative Tree, and Applications to Kato Varieties","description":"\u003cp\u003eThis thesis deals with specific features of the theory of holomorphic dynamics in dimension 2 and then sets out to study analogous questions in higher dimensions, e.g. dealing with normal forms for rigid germs, and examples of Kato 3-folds.\u003c\/p\u003e\u003cp\u003eThe local dynamics of holomorphic maps around critical points is still not completely understood, in dimension 2 or higher, due to the richness of the geometry of the critical set for all iterates.\u003c\/p\u003e\u003cp\u003eIn dimension 2, the study of the dynamics induced on a suitable functional space (the valuative tree) allows a classification of such maps up to birational conjugacy, reducing the problem to the special class of rigid germs, where the geometry of the critical set is simple.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eIn some cases, from such dynamical data one can construct special compact complex surfaces, called Kato surfaces,\u003cbr\u003erelated to some conjectures in complex geometry.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e","brand":"Scuola Normale Superiore","offers":[{"title":"Default Title","offer_id":47060758003952,"sku":"9788876425585","price":24.99,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9788876425585_p0.jpg?v=1769835755","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9788876425585","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}