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001 978-3-0346-0048-4
003 DE-He213
005 20181204133145.0
007 cr nn 008mamaa
008 100301s2009 sz | s |||| 0|eng d
020 _a9783034600484
_9978-3-0346-0048-4
024 7 _a10.1007/978-3-0346-0048-4
_2doi
040 _aISI Library, Kolkata
050 4 _aQA564-609
072 7 _aPBMW
_2bicssc
072 7 _aMAT012010
_2bisacsh
072 7 _aPBMW
_2thema
082 0 4 _a516.35
_223
100 1 _aItenberg, Illia.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aTropical Algebraic Geometry
_h[electronic resource] /
_cby Illia Itenberg, Grigory Mikhalkin, Eugenii Shustin.
264 1 _aBasel :
_bBirkhäuser Basel,
_c2009.
300 _aIX, 104 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aOberwolfach Seminars,
_x1661-237X ;
_v35
505 0 _aPreface -- 1. Introduction to tropical geometry - Images under the logarithm - Amoebas - Tropical curves -- 2. Patchworking of algebraic varieties - Toric geometry - Viro's patchworking method - Patchworking of singular algebraic surfaces - Tropicalization in the enumeration of nodal curves -- 3. Applications of tropical geometry to enumerative geometry - Tropical hypersurfaces - Correspondence theorem - Welschinger invariants -- Bibliography.
520 _aTropical geometry is algebraic geometry over the semifield of tropical numbers, i.e., the real numbers and negative infinity enhanced with the (max,+)-arithmetics. Geometrically, tropical varieties are much simpler than their classical counterparts. Yet they carry information about complex and real varieties. These notes present an introduction to tropical geometry and contain some applications of this rapidly developing and attractive subject. It consists of three chapters which complete each other and give a possibility for non-specialists to make the first steps in the subject which is not yet well represented in the literature. The intended audience is graduate, post-graduate, and Ph.D. students as well as established researchers in mathematics.
650 0 _aGeometry, algebraic.
650 1 4 _aAlgebraic Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M11019
700 1 _aMikhalkin, Grigory.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aShustin, Eugenii.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783034601313
776 0 8 _iPrinted edition:
_z9783034600477
830 0 _aOberwolfach Seminars,
_x1661-237X ;
_v35
856 4 0 _uhttps://doi.org/10.1007/978-3-0346-0048-4
912 _aZDB-2-SMA
942 _cEB
950 _aMathematics and Statistics (Springer-11649)
999 _c426158
_d426158